Answers
Answer:
y ≈ 15272.9(1.06306^x) . . . . from regression tool
y = 15300(1.0624^x) . . . . calculated "by hand"
Step-by-step explanation:
An exponential model is one that uses the exponential function ...
f(x) = a·b^x
to model the data. The value of 'a' is the function value when x=0, the initial value. The value of 'b' is the growth factor, the multiplier between function values for successive values of x.
__
toolAn exponential regression tool makes short work of this. Such tools are available on some calculators, apps, and spreadsheets. All that is required is entering the data into a table and invoking the tool. The one shown in the attachment tells you the model is approximately ...
y ≈ 15272.9(1.06306^x)
__
averagingWe can average the growth rate factors a couple of different ways. When we think of "averaging," we usually think of the arithmetic mean, the sum of values divided by their number. If we average the growth rates in this way, we get ...
average rate of growth =
((161/153) +(173/161) +(184/173) +(196/184) +(207/196) +(220/207))/6 ≈ 1.0624
Using the first table value as the initial value, the model formed this way is ...
y = 15300(1.0624^x)
__
For exponential growth it may make more sense to compute the geometric mean. This is the n-th root of the product of n numbers. In this case, it reduces to the 6-th root of the ratio of the last to the first:
average rate of growth = (220/153)^(1/6) ≈ 1.0624
This gives the same growth factor as above, hence the same model.
The second attachment shows the application of this model to the domain used in the table. We see there are some minor differences when rounding the function value to the nearest hundred.
The differences in our two models seem to arise from rounding the data values in the table to the nearest hundred.
__
summaryThe values given in the table can be used in different ways to arrive at two similar, but different exponential models of the table data:
y = 15272.9(1.06306^x)y = 15300(1.0624^x)Interestingly, the function calculated "by hand" has a very slightly better correlation with the table data. The difference in correlation coefficients is in the 6th decimal place.
Related Questions
the volume of a cube depends on the length of its sides.this can be written in function notation as v(s). what is the best interpretation of v(4) =64
Answers
Answer:
Interpretation: A cube with sides of 4 units each has a volume of 64 units³.
Explanation:
As v(s) represents the volume of the cube, s represents the length of the sides.
∴ v(4) represents the volume of a cube with sides of units, and the volume is 64 units³
-750 DEGREE TO RADIAN
Answers
2pi = 360 degree
If we divide 360 by 2
Pi = 180 degrees
To find 1 radian in degree
180/pi
Cause
Pi = 180 degree
/pi /pi
1 radian = 189/ pi
Equations Of Parabolas (Conics) Unscramble
Answers
The match is shown in the picture for the function of a parabola and the graph of a parabola.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
As we know the standard form of the parabola is:
y = a(x - h)² + k
If a > 0 (parabola opens upwards)
If a < 0 (parabola opens downwards)
or
x = a(y - h)² + k
If a > 0 (parabola opens right side)
If a < 0 (parabola opens left side)
Here (h, k) is the vertex of the parabola and a is the leading term.
Thus, the match is shown in the picture for the function of a parabola and the graph of a parabola.
Learn more about the parabola here:
brainly.com/question/8708520
#SPJ1
manual spent 4.56 on a sandwich and 2.98 on a drink How much did he spend in all? If he paid with a 10$ bill how much change did he get
Answers
Manual paid with a $10 bill and he got $2.46 as a change.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.
Money spent on sandwich=$4.56 and money spent on drink=$2.98.
We need to find out how much did he spend in all.
That is, the total money spent=4.56+2.98=$7.54
He paid with a $10 bill, he gets change as 10-7.54=$2.46
Hence, he paid with a $10 bill and he got $2.46 as a change.
To learn more about subtraction visit:
https://brainly.com/question/1927340.
#SPJ1
if 300 equals 9 and 500 equals 16 what is the pattern? and what will 7 and 18 equal?
Answers
Step-by-step explanation:
hope you can understand
Which expression is equivalent to...
Answers
Answer:
p^2/r
Step-by-step explanation:
so I have shown every work in the picture attached
please let me know if this doesn't help
what are the coordinates of this point help plssssssssssssssss
Answers
Answer:
(-2, -4)
Step-by-step explanation:
Use the (x,y) thing:
x = -2
y = -4
therefore, (-2, -4)
The graphs below have the same shapes. What is the equation for the red graph?
Answers
The function g(x) is derived by translating the function by the three units, according to the graph.The equation for the red graph will be,g(x) = x²+3
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
From the graph, it is obtained that the function g(x) is obtained by translating the function by the three units.
Hence,the equation for the red graph will be,g(x) = x²+3
To learn more about the graph, refer to the link;
https://brainly.com/question/14375099
#SPJ1
Question 7 of 10 Which system of inequalities is graphed below? 10 -10 -8- 8 10 OA. y > X - 4 y < x +6 OB. VS X - 4 y < x +6 O c. y2 x -4 y > x + E OD. VS X - 4 y > x2 + 6
Answers
Because in both graphs the shaded region is above the curve, the correct option is C.
Which pair of inequalities is graphed?
On the graph we can see two parabolas, such that the y-intercepts of these are:
y = 6
y = -4
So we just need to find the pair of options with these y-intercepts, and noticing that for both cases, we must have:
y > parabola.
Because both shaded regions are above the parabolas.
The only option that meets these requirements is option C. Where there is a mistake, as you can see both curves have dashed lines, and always when we have dashed lines we should use the symbols > or <, while in that option we have a ≥ symbol
If you want to learn more about inequalities:
https://brainly.com/question/18881247
#SPJ1
I'm a kid. and I'm starting 4th grade so I lied to the computer, Anyhoo. Can anyone PLS help me comvert 6/7.
Answers
6/7 converted to a decimal is 0.8571
Conversion to decimalsFrom the question, we are to convert the given fraction to a decimal
The given fraction is
6/7
6/7 = 0.8571
Thus,
6/7 expressed as a decimal is 0.8571
Hence, 6/7 converted to a decimal is 0.8571
Learn more on Conversion to decimals here: https://brainly.com/question/15271387
#SPJ1
URGENT 30 points I need help
Answers
Answer:
- 112 + 100 n
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
~~~~~~~
[tex]a_{1}[/tex] = - 12
d = 100
[tex]a_{n}[/tex] = - 12 + 100( n - 1 )
[tex]a_{n}[/tex] = - 12 + 100n - 100
[tex]a_{n}[/tex] = - 112 + 100 n
y=2x^2-4x-3
Solve quadratic questions
Answers
By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.
How to find the roots of a quadratic equation
All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex] (1)
If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:
[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]
[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]
[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]
By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.
To learn more on quadratic equations: https://brainly.com/question/2263981
#SPJ1
Find the x- and y-intercepts of the parabola y=x2+10x+4
Answers
Answer:
x-intercepts: -5 +/-[tex]\sqrt{21}[/tex]. y-intercept: 4
Step-by-step explanation:
For x-intercepts use the quadratic equation
[tex]x= (-b +/-\sqrt{b^2-4ac} )/2a[/tex]
Fill in your values:
[tex]x= (-10 +/-\sqrt{100-16} )/2[/tex]
And solve
[tex]x=-5 +/- \sqrt{21}[/tex]
For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.
PLEASE HELP
Write a rational function that meets the following criteria. Leave your answer in factored form.
• Vertical asymptote at x = -2
• Horizontal asymptote at y = 3 and a hole at x = -3
Answers
Answer:
Step-by-step explanation:
Renate launched an object vertically from a point that is 58.9 meters above ground level with an initial velocity of 21.6 meters per second. This situation can be represented by the equation h=−4.9t2+21.6t+58.9, where h is the height of the object in meters and t
is the time in seconds after the object is launched.
What is the maximum height of the object?
Answers
The maximum height of the object is 82.7034 from the ground
What is Velocity ?Velocity is the measure of movement of an object with respect to time.
It is measured in m/sec
h = -4.9t²+21.6t +58.9
dh/dt = -9.8t +21.6
At maximum height , velocity = 0
therefore
-9.8t +21.6 = 0
9.8t = 21.6
t = 2.204 sec
h = -4.9 (2.204)²+ 21.6 * 2.204 +58.9
h = -23.803 +47.606 +58.9
h = 82.7034 from the ground
h = 23.80 from the point it is launched.
The maximum height of the object is 82.7034 from the ground
To know more about Velocity
https://brainly.com/question/18084516
#SPJ1
2 more than product of a number and 9 is 8. variable w
Answers
Answer:
w (number) = 2/3
Step-by-step explanation:
Variable w means use the letter w as the unknown number :
This is the equation made from the question :
2+(9w) = 8
Let's subtract 2 from both sides :
9w = 6
Divide both sides by 9 :
w = 6/9
Simplify fraction :
w = 2/3
Hope this helped and have a good day
write a linear function of f with f(-3)=-2 and f(-2)=3
Answers
Answer:
y=5x+13
Step-by-step explanation:
when x=-3, y=-2, and when x=-2, y=3. we know that every time x increases by 1, y also increases by 5. This means that the slope is 5. to find the y-intercept, we need x to be 0. to find that, increase x by 2. if x increases by 2, then y would also increase by 10. add 10 to 3 and add 2 to -2 to get x=0 and y=13. the coordinates would be (0,13). the y-intercept is 13. now that we have enough information, we can conclude that y=5x+13. To check your answer, plug in the values for x.
Each serving of a cereal is 80 calories.which expression can be used to find the number of calories In 3 servings
Answers
Answer:
[tex]80\times3[/tex]
Step-by-step explanation:
Based on the given conditions, formulate: [tex]80\times3[/tex]
Calculate the product or quotient: 240
get the result: 240
Answer: 240
To find this answer, we had to use the expression 80 * 3, therefore making it the answer.
Answer:
240
Step-by-step explanation:
80*3=240
so u multiply the equation
Use the graph to write the inequality that represents the shaded region
Answers
Answer:
4/2 is the wrong answer
Step-by-step explanation:
because it is
Find the time diffrence.
If u click there will be pic (very easy im just lazy lol)
Answers
Step-by-step explanation:
2 hours and 45 minutes.
8:45am + 2 hours = 10:45am
10:45am + 45 minutes = 11:30 am
What is the solution of
x²-1
2
x2 +5X+4
<0?
Answers
Answer:
Step-by-step explanation:
What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solution
Answers
The solution to the system of equation is (-4 , 2) , Option A is the right answer.
What are System Of equation ?A set of equation whose factors are common are called system of equations.
It is given in the question
3x +5y = -2
3x +7y = 2
On solving this we get
-2y = -4
y = 2
On substitution in any equation
x = -4
Therefore solution to the system of equation is (-4 , 2) , Option A is the right answer.
To know more about System of equation
https://brainly.com/question/12895249
#SPJ1
Answer:
A.
Step-by-step explanation:
took tha quiz
Which is the equation of the line with slope 0 passing through the point (-3, -1)?
Answers
4. Use the formula for the area of a circle to derive the formula for the area of a sector.
Answers
The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).
What is the area of the sector?Let r be the radius of the circle. Then the area of the circle will be
Area = πr²
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
Area = (θ/2π) x (area of the circle)
More about the area of the sector link is given below.
https://brainly.com/question/7512468
#SPJ1
I’m so confused on what numbers l should put into the boxes
Answers
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The lines for the given statements can be plotted as shown below.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The lines for the given statements can be plotted as shown below.
The coordinate grid can be filled as,
1)
x 0 3 1
y 3 0 2
2.)
x 0 1 -1
y 1 0 2
3.)
x 0 4 -1
y -2 0 2
4.)
x 0 1 1
y -2 0 -2
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ1
Which is the graph of f(c)=1/4(4)^x?
Answers
Answer: The graph shown
Step-by-step explanation:
Another graph of the function is attached in this answer.
Tickets for a county fair are $8 for an adult and $5 for a child. If you have a 15% discount card, how
much will 2 adult tickets and 2 child tickets cost?
Answers
Answer:
$21.25
Step-by-step explanation:
The cost of the 2 adult tickets before the discount is $8 * 2 = $16
The cost of the 2 child tickets before the discount is $5 * 2 = $10
The total cost before the discount is $16 + $10 = $26
The total cost after the discount is
$26 * (1 - 0.15) =
$26 * 0.85 =
$21.25
The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
Answers
If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.
Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.
We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].
Volume which is given as 13685 cubic inches.
13685=π[tex]r^{2}h[/tex]
π=22/7
13685=π[tex](11)^{2}[/tex]h
h=13685*7/22*121
h=95795/2662
h=35.98
if we round it to nearest tenth then the value of h be 36 inches.
Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.
Learn more about volume at https://brainly.com/question/463363
#SPJ10
Answer:36
Step-by-step explanation:
3
cky has a board that is 2 feet long. She needs to cut the board into 11 pieces of equal length. How long
ould each piece be?
0.223 feet
0.25 feet
0.5 feet
0.75 feet
ase select the best answer from the choices provided
A
В
C
D
Answers
Answer:
0.223 is the answers for the question but I got this answer 0.181
Step-by-step explanation:
please mark me as brainlest
The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 25 ounces and a standard deviation of 0.8 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?
Answers
The percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
What is the z score?The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.
Given data;
Mean,μ = 25
Standard deviation,σ=0.8
The Z score is found as;
[tex]\rm Z = \frac{x-\mu}{ \sigma } \\\\ Z = \frac{24-25}{0.8} \\\\ Z= -1.25[/tex]
The P-value for the obtained z score is .2113.
Hence the percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
To learn more about the Z score, refer to;
https://brainly.com/question/15016913
#SPJ1
