Math question help!!!!

Question

The population of a specific bacteria growing in a Petri dish is modelled by the function p(t)=5000(2)^t/8 , where p(t) represents the number of bacteria and trepresents the time, in days, after the initial time. How long does it take for the population to double?

a) 8

b) 1

c) 2

d) 9

Answer 1

Since the population starts at 5000, set p(t)=10000 and solve for t.

10000 = 5000 (2)^t/8

2 = (2)^t/8

Take log base 2 of both sides.

log₂2 = (t/8) log₂2

1 = t/8

t = 8 days