Chapter 7.6, Problem 15P

A population of amoebas in a petri dish will triple in size every 20 minutes. At the start of an experiment the population is 800. The function $y=800\cdot 3^x$

where $x$ is the number of 20 minute periods, models the population growth. How many amoebas are in the petri dish after 3 hours?

To determine

To find the number of amoebas in the petri dish after 3 hours.

Answer to Problem 15P

1,57,46,400.

Explanation of Solution

Given:

The function $y=800\cdot 3^x$ models the population growth of amoebas, where $x$ is the number of 20 minute periods.

Calculation:

  $\begin{array}{l}3\text{hours}=180\text{minutes}\\ =9\times 20\text{minutes}\end{array}$

Therefore there are 9 twenty minute periods in 3 hours.

So put $x=9$ in $y=800\cdot 3^x$ , we get

  $\begin{array}{l}y=800\cdot 3^9\\ =1,57,46,400\end{array}$

Hence there are 1,57,46,400 amoebas in the petri dish after 3 hours.