Question

A virus takes 8 days to double its original population (A=2A0). How long will it take to quadruple its population? Round to the nearest tenth.

Answer 1

Answer:

It takes 16 days to quadruple its population.

Step-by-step explanation:

The population of the virus can be represented by the following exponential function.

$A(t) = A_{0}e^{rt}$

In which A(t) is the population after t days, $A_{0}$ is the initial population and r is the growth rate.

In this problem, we have that:

$A(8) = 2A_{0}$

So, we use this to find the value of r.

$A(t) = A_{0}e^{rt}$

$2A_{0} = A_{0}e^{8r}$

$e^{8r} = 2$

Applying ln to both sides

$8r = 0.6931$

$r = 0.0867$

How long will it take to quadruple its population?

This is t when $A(t) = 4A_{0}$

$A(t) = A_{0}e^{rt}$

$4A_{0} = A_{0}e^{0.0867t}$

$e^{0.0867t} = 4$

Again we apply ln to both sides.

$0.0867t = 1.39$

$t = 16$

It takes 16 days to quadruple its population.