Question

Lavania is studying the growth of apopulation of fruit flies in her laboratory. She noticesthat the number of fruit flies in her experiment is fivetimes as large after any six-day period. She observes 20fruit flies on October 1. Write and evaluate anexpression to predict the population of fruit fliesLavania will observe on October 31.

Answer 1

Lavania is studying the growth of a

population of fruit flies in her laboratory. She notices

that the number of fruit flies in her experiment is five

times as large after any six-day period. She observes 20

fruit flies on October 1. Write and evaluate an

expression to predict the population of fruit flies

Lavania will observe on October 31.

`P=p(1+i)^(^n)`

by the question data

Let

p=the initial population = x

five times as large= 5x

n= number of periods = 6

`\begin{gathered} 5x=x(1+i)^6 \\ 5=(1+i)^6 \\ \sqrt[6]{5}=\text{ }\sqrt[6]{(1+i)^6} \\ \sqrt[6]{5}=1+i \\ \sqrt[6]{5}-1=i \\ 0.3076=\text{ i} \end{gathered}`