A bacteria culture doubles every 15 mins.

Question

How long will it take for a culture of 20 bacteria to grow to a population of 163840?

Answer 1

This is an example of exponential growth.

t = time in minutes

p(t) = population at time t

p₀ = initial population

p(t) = p₀ (2)^t/15

p(t) = 20 (2)^t/15

Set p(t)=163840 and solve for t.

163840 = 20 (2)^t/15

(163840 / 20) = (2)^t/15

log(163840 / 20) = (t/15) log2

You should be able to solve for t and finish from here. The log can be in any base as long as you use the same base in both places in the equation.