Question

A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 4 hours there will be 1040 bacteria.

(a) Express the population after t hours as a function of t.

this is what i put as my answer but i guess its not right do i replace the four with t??


260e^tln4/4

Answer 1

The population apparently doubles in 2 hours.

P = 260 * 2^(t/2) is a simpler way to write it.

Note that e^(t ln4/4)= [e^(ln4)]^(t/4)
= 4^(t/4)= [2^2]^(t/4) = 2^(t/2)

Your version is apparently correct, but needs to be simplified