Question

A bacteria culture starts with 1,500 bacteria and doubles in size every 2 hours. How do you find an exponential model for the size of the culture as a function of time t in hours?

Answer 1

`s(t)=1500 * 2^(t/2)`

Explanation:

If the culture has a growth rate, `r` such that it doubles in size every `color(red)2` hours, then
`color(white)("XXX")r^color(red)2=2`
`rarr`
`color(white)("XXX")r=sqrt(2)`

and, given an initial size of `1,500` bacteria, its size after `t` hours would be:
`color(white)("XXX")s(t)=1500 * (sqrt(2))^t` or `1500 * 2^(t/2)`