Chapter 8, Problem 5MCQ

(a)

To determine

To find: The exponential function that could be used to model the number of bacteria after $x$ hours.

Answer to Problem 5MCQ

The exponential function is $y=6000{\left(2.16\right)}^x$

Explanation of Solution

Given:

The given information is:

The population started originally with $6000$ bacteria cells.

After $2$ hours, there were $28000$ bacteria cells.

The exponential form is calculated as:

  $\begin{array}{c}6000{\left(r\right)}^2=28000\\ {\left(r\right)}^2=\frac{28000}{6000}\\ {\left(r\right)}^2=4.66\\ r=2.16\end{array}$

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

  $y=6000{\left(2.16\right)}^x$

(b)

To determine

To find: The number of bacteria can be expected after $4$ hours.

Answer to Problem 5MCQ

The number of bacteria can be expected after $4$ hours is $130,608$ bacteria.

Explanation of Solution

To find the number of bacteria can be expected after $4$ hours is calculated by substituting $x=4$ in the exponential function in the first part.

The number of bacteria can be expected after $4$ hours is calculated is:

  $\begin{array}{c}y=6000{\left(2.16\right)}^x\\ y=6000{\left(2.16\right)}^4\\ y=6000\left(21.768\right)\\ y=130,608\end{array}$

Therefore the number of bacteria can be expected after $4$ hours is $130,608$ bacteria.