Question

A virus takes 6 days to double its original population (A=2A0). How long will it take to triple its population? Round to the nearest tenth.

Answer 1

Answer:

9.5 days

Step-by-step explanation:

-This problem can be modeled using an exponential function of the form:

$A=A_oe^{rt}\\\\A=Population \ at \ time\ t\\A_o=Initial \ Population\\r-Growth \ rate\\t=time$

#We equate to solve for r:

$A=A_oe^{rt}, A=2A_o\\\\\therefore 2=e^{6r}\\\\\\r=\frac{In \ 2}{6}\\\\=0.1155$

#we then use this calculate this growth rate to calculate t when A=$3A_o$:

$A=A_oe^{rt}, A=3A_o\\\\3=e^{0.1155t}\\\\t=\frac{In \ 3}{0.1155}\\\\=9.5118\approx 9.5 \ days$

Hence, it takes approximately 9.5 days for the population to triple.