Question

A bacteria population grows by 10% every 2 years. Presently, the population is 80 000 bacteria. Find the population in 8 years from now. (Can use log if needed but not “in”)

Answer 1

An exponential function is modeled using the equation:

`P(t)=a(1+r)^{(t)/(n)}`

where P(t) is the population after t years, a is the initial population, r is the growth rate in decimals, t is the number of years, and n is the number of periods in one cycle.

From the given information, we have the following parameters:

`\begin{gathered} a=80000 \\ r=0.1 \\ t=8 \\ n=2 \end{gathered}`

Therefore, the population after 8 years can be calculated by substituting into the formula and solving for P(t) as follows:

`\begin{gathered} P(t)=80000(1+0.1)^{(8)/(2)}=80000(1.1)^4 \\ P(t)=117128 \end{gathered}`

The population is 117,128.