Question

The size of an exponentially growing bacteria colony doubles in 2 hours. How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form. Exact form

Answer 1

Exponential growth and the double growth indicates the population size is modeled by
\[y=a(2^{rx})\]
with \(a\) being the initial population, \(r\) being the relative growth factor, and \(x\) is time.

The population doubles in 2 hours, so when \(x=2\), you have
\[2a=a2^{2r}\\
2=2^{2r}\\
1=2^{2r-1}\\
r=\frac{1}{2}\]
So you have to find \(x\) such that \(y=3a\):
\[3a=a\left(2^{x/2}\right)\]
Sounds right, at any rate. I might be wrong.

Answer 2

If it doubles every 2 hours then formula is
2^((t-2)/2)

you want to solve when 2^((t-2)/2) = 3

Answer 3

@wolf1728 So i solve 2^((t-2)/2)=3 ?

Answer 4

for t?

Answer 5

Is this right?