Question

A biologist is observing the exponential growth pattern of a virus. She starts with 60 of the virus that grows at a rate of 20% per hour. She will check on the virus in 24 hours. How many viruses will she find? (Simplify your answer completely. Round your answer to the nearest whole number.)

Answer 1

Since they grow exponentially, the number of viruses after t hours is given by the function:

$f(t)=f(0)\cdot(1+r)^t$

where f(0) is the initial number of viruses and r is the rate of growth.

In this problem, we have:

$\begin{gathered} f\mleft(0\mright)=60 \\ \\ r=20\%=\frac{20}{100}=0.2 \end{gathered}$

And after 24 hours, t = 24. So, the number of viruses she will find is f(24):

$f(24)=60\cdot(1+0.2)^{24}=60\cdot1.2^{24}\cong4770$

Therefore, rounding to the nearest whole number, the answer is 4770 viruses.