Chapter 8.6, Problem 30E

(a)

To determine

To describe: The type of function.

Answer to Problem 30E

The function is an exponential function

Explanation of Solution

Given information:

A table consisting of speed and breathing rate is given

Calculation:

The plot is given below

  

Even though the points are in a line, there is no common difference between the values in the table. But there is common ratio of 1.1 between the values of the table. And thus the function is an exponential function

Conclusion:

The function is an exponential function

(b)

To determine

To describe: a function that models the data

Answer to Problem 30E

The function will be $f\left(x\right)=6.4{\left(1.11\right)}^x$

Explanation of Solution

Given information:

A table consisting of speed and breathing rate is given

Calculation:

The general form of an exponential function is as follows:

  $y=a{b}^x$

The common ratio in this case is 1.1 and thus $b=1.11$

To solve for ‘a’, consider any points such as $(20,51.4)$

Then,

  $\begin{array}{l}51.4=a{\left(1.11\right)}^{20}\\ a=\frac{51.4}{{1.11}^{20}}\approx 6.4\end{array}$

Therefore the required function will be

  $f\left(x\right)=6.4{\left(1.11\right)}^x$

Conclusion:

The function will be $f\left(x\right)=6.4{\left(1.11\right)}^x$

(c)

To determine

To find: the breathing rate of the cyclist

Answer to Problem 30E

41.9 liters of air per minute

Explanation of Solution

Given information:

The cyclist travels at 18 miles per hour

Calculation:

Substituting the $x=18$ in the formula $f\left(x\right)=6.4{\left(1.11\right)}^x$

  $f\left(x\right)=6.4{\left(1.11\right)}^{18}$

  $f\left(x\right)\approx 41.9$

41.9 liters of air per minute

Conclusion:

41.9 liters of air per minute