Chapter 7.4, Problem 7MCQ

(a)

To determine

To find: The exponential function that could be used to model the population of the city $x$ years after $1995$ .

Answer to Problem 7MCQ

The exponential function is $y=45000{\left(1.035\right)}^x$ .

Explanation of Solution

Given:

The given information is:

The population was $45000$ in $1995$ .

In $2007$ , the population was $68000$ .

The exponential form is calculated as:

  $\begin{array}{c}45000{\left(r\right)}^{2007-1995}=68000\\ {\left(r\right)}^{12}=\frac{68000}{45000}\\ r={\left(\frac{68000}{45000}\right)}^{\frac{1}{12}}\\ r=1.035\end{array}$

Therefore the exponential function that could be used to model the number of bacteria after $x$ hours is given as:

  $y=45000{\left(1.035\right)}^x$ .

(b)

To determine

To find: The total population in $2015$ .

Answer to Problem 7MCQ

The total number population in $2015$ was $679950$ .

Explanation of Solution

To find the total number population in $2015$ can be expected after $12$ years is calculated by substituting $x=12$ in the exponential function in the first part.

The number of bacteria can be expected after $12$

years is calculated is:

  $\begin{array}{c}y=45000{\left(1.035\right)}^x\\ y=45000{\left(1.035\right)}^{12}\\ y=45000\left(1.511\right)\\ y=679950\end{array}$

Therefore the total number population in $2015$ was $679950$ .