Question

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

Answer 1

The correct answer is:

46.6 days

Explanation:

The general form for exponential growth is

$A=p(1+r)^t$, where A is the total amount, p is the initial amount, r is the percent of growth, and t is the amount of time (in this case, days).

We do not know the initial amount, the total amount, or the amount of time.  We do know that r, the percent of growth, is 1.5%; 1.5% = 1.5/100 = 0.015:

$A=p(1+0.015)^t$

We also know we want the total amount, A, to be twice that of the initial amount, p:

$2p = p(1+0.015)^t \\ 2p=p(1.015)^t$

Divide both sides by p:

$\frac{2p}{p}=\frac{p(1.015)^t}{p} \\ \\ 2=1.015^t$

Using logarithms to solve this,

$\log_{1.015}(2)=t \\ \\46.6=t$

Answer 2

Sorry, I tried to answer with a full explanation but the equation function on brainly.com stopped working. Now I can't delete my attempt at an answer with explanation. The correct answer is 46.6 days.