In addition to quadratic and exponential models, another common type of model is called a power model. Power models are models in the form

a2linetagadaW
2021-01-06
Answered

In addition to quadratic and exponential models, another common type of model is called a power model. Power models are models in the form

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BleabyinfibiaG

Answered 2021-01-07
Author has **118** answers

Step 1Note: The solution gives the commands for the calculation using aTi83/84-calculator. If you use a different type of technology, then the commands will differ.Press on STAT and then select 1:Edit ... Enter the data of distance from the sun in the list $L}_{1}\text{}\text{and enter the data of period of revolution in the list}\text{}{L}_{2$ .Next, press on STAT, select CALC and then select ${P}_{WT}\text{}{R}_{eg}.\text{}\text{Next, we need to finish the command by entering}\text{}{L}_{1},\text{}{L}_{2}.$

$P}_{WT}\text{}{R}_{eg}\text{}{L}_{1},\text{}{L}_{2$ Finally, pressing on ENTER then gives us the following result:$y=a\text{}\cdot \text{}{x}^{b}$

$a=1.003$

$b=1.4998$

${r}^{2}=1$ This then implies that the regression line is:$\hat{y}=a\text{}\cdot \text{}{x}^{b}=1.0003\text{}\cdot \text{}{x}^{1.4998}$ where x represents the distance from sun and y represents the period of revolution.Step 2Given:$x=30.061$

$y=164.810$ Evaluate the equation of the regression line at $x=30.061:$

$\hat{y}=1.0003\text{}\cdot \text{}{30.061}^{1.4998}\text{}\approx \text{}164.7631$ The residual is the difference between the observed y-value and the predicted y-value.$\text{Residual}\text{}=y\text{}-\text{}\hat{y}\text{}=164.810\text{}-\text{}164.7631=0.0469$ Neptune's period of revolution is 0.0469 earth years longer than expected.

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(a) Find a function that models the population t years after 1990.

(b) Find the time required for the population to double.

(c) Use the function from part (a) to predict the population of California in the year 2010. Look up California’s actual population in 2010, and compare.

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