A virus takes 13 days to double its original population (A=2A0). How long will it take to triple its population? Round to the nearest tenth. Approximate the answer.
t≈20.6

This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the time it takes the population to triple.
Identify the variables in the formula.
AA0ktA=2A0=?=?=13 days=A0ekt
Substitute the values in the formula.
2A0=A0ek⋅13
Solve for k. Divide each side by A0.
2A0A0=e13k
Take the natural log of each side.
ln2=lne13k
Use the power property.
ln2=13klne
Simplify.
ln2=13k
Divide each side by 13.
ln213=k
Approximate the answer.
k≈0.053
We use this rate of growth to predict the time it takes the population to triple.
AA0ktA=3A0=?=ln213=?=A0ekt
Substitute in the values.
3A0=A0eln213⋅t
Solve for t. Divide each side by A0.
3=eln213⋅t
Take the natural log of each side.
ln3=lneln213⋅t
Use the power property.
ln3=ln213tlne
Simplify.
ln3=ln213t
Multiply each side by 13 and divide each side by ln2.
13ln3ln2=t
Approximate the answer.
t≈20.6

The time it takes the virus population to triple is at least 20.6 days.