1. ## Exponential growth

A formula for the rate of chnage in population of a colony of bacteria is given by $\displaystyle P=3200 + 400e^{kt}$

If the population doubles after 20 hours, how long will it take to triple the original population?

2. Originally Posted by nerdzor
A formula for the rate of chnage in population of a colony of bacteria is given by $\displaystyle P=3200 + 400e^{kt}$

If the population doubles after 20 hours, how long will it take to triple the original population?
You are given that the population doubles after 20 hours:

$\displaystyle 6400 = 3200 + 400e^{20k}$

Solve for k.

Then plug k into your solution with the original amount tripled:

$\displaystyle 9600 = 3200 + 400e^{kt}$

*Solve for t!