Chapter 11.3, Problem 6CFU

(a)

To determine

To find: Whether the Bakersfield’s population experienced the growth or the decline.

Answer to Problem 6CFU

The growth is exponential.

Explanation of Solution

Given:

The model for the equation of the city model is,

  $y=33,430e^{0.0397t}$

Calculation:

Consider the exponential growth in terms of $e$ is,

  $N=N_0{e}^{kt}$

Then, from the above equation and the given equation the required values are,

  $\begin{array}{l}N=y\\ N_0=33430\\ k=0.0397\\ t=\text{time}\end{array}$

Since, the value of the k is positive the population growth is exponential.

Hence, the growth is exponential.

(b)

To determine

To find: The Bakersfield’s population in 1950.

Answer to Problem 6CFU

The required population is $34784$ .

Explanation of Solution

Given:

The model for the equation of the city model is,

  $y=33,430e^{0.0397t}$

Calculation:

Consider model for the equation of the city model is,

  $y=33,430e^{0.0397t}$

Then, pollution in the year 1950 is,

  $\begin{array}{c}y=33,430e^{0.0397\left(1\right)}\\ =34784\end{array}$

(c)

To determine

To find: The projected population of the Bakersfield in 2010.

Answer to Problem 6CFU

The required population is $361931$ .

Explanation of Solution

Given:

The model for the equation of the city model is,

  $y=33,430e^{0.0397t}$

Calculation:

Consider model for the equation of the city model is,

  $y=33,430e^{0.0397t}$

Consider the number of years between 2010 and 1950 is 60.

Then, pollution in the year 2010 is,

  $\begin{array}{c}y=33,430e^{0.0397\left(60\right)}\\ =361931\end{array}$