Math question #6

Question

The population of a specific bacteria growing in a Petri dish is modeled by the function: 

p(t) = 5000 (2)^t/3

Where p(t) represents the number of bacteria and t represents the time, in days, after the initial time. Determine the time when the population is 40 000

a.) 24

b) 6

c) 9

d) 3

Answer 1

We are given P(t) = 40000 and are asked to solve for the time, t, at which this 40000 bacteria are present. We can substitute 40000 into the left hand side of the equation to get: 40000 = 5000(2)^t/3. Dividing both sides by 5000 we get: 8 = 2^t/3. Now note that 8 is equivalent to 2³. Thus we rewrite the equation as follows: 2³ = 2^t/3. Thus t/3 = 3 which when we solve we get t = 9, which is choice c).