Question

A. Write an exponential function to model with population Y of bacteria X hours after 2 PM

B. How many bacteria were there at 7 PM that day

Answer 1

In this problem, we have an exponential growth function of the form

`y=a(b)^x`

where

a=10 bacteria (initial value at 2 pm)

b is the base of the exponential function

`y=10(b)^x`

Find out the value of b

we know that

For x=0 (2 pm), y=10 bacteria

At 5 pm

y=33,750 bacteria

x=(5 pm-2 pm)=3 hours

substitute in the exponential equation

`33,750=10(b)^3`

Solve for b

`b^3=(33,750)/(10)`
`\begin{gathered} b=\sqrt[3]{(33,750)/(10)} \\ b=15 \end{gathered}`

the equation is

`y=10(15)^x`

Part B

At 7 pm

x=(7 pm-2 pm)=5 hours

substitute

`\begin{gathered} y=10(15)^5 \\ y=7,593,750\text{ bacteria} \end{gathered}`