Chapter SH, Problem 7.18EP

a.

To determine

To find the annual percentage decrease of the population.

Answer to Problem 7.18EP

  $5\%$ .

Explanation of Solution

Given:

The given table is

  

Calculation:

The decrease in the population of wolf from $2005$ to $2006$ is,

  $\begin{array}{l}=420-399\\ =21\end{array}$

So, the percentage decrease will be,

  $\begin{array}{l}=\frac{21}{420}\times 100\\ =5\%\end{array}$

Hence, the annual percentage decrease is $5\%$ .

b.

To determine

To write the logarithmic function for the time in years.

Answer to Problem 7.18EP

  $y=425.527-47.548\ln x$ .

Explanation of Solution

Given:

The function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$

Calculation:

Use Ti-82 to solve find logarithmic function,

Press STAT

  

Now, press $1$ and enter the data in the following window,

  

Now, go to CALC and choose LNREG

  

Press ENTER

  

So, the logarithmic function that defines the population will be

  $\begin{array}{l}y=a+b\ln x\\ a=425.527\\ b=-47.548\end{array}$

c.

To determine

To find the number of wolves in $2020$ .

Answer to Problem 7.18EP

  $293.69$ .

Explanation of Solution

Given:

The function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$

Calculation:

Number of wolves in $2020$ will be,

Consider the following expression,

  $\begin{array}{l}y=a+b\ln x\\ a=425.527\\ b=-47.548\end{array}$

Substitute the value of $x=16$ as in the above expression,

  $\begin{array}{l}y=425.527-47.548\ln x\\ y=425.527-47.548\ln 16\\ y=293.69\end{array}$

Hence, the population of wolf in the year will be $293.69$