calculus math question

Question

The population of a bacteria culture doubles every 0.5 hours. An experiment begins with 620 bacteria. 

a) Determine the number of bacteria after

i) 3 hours ii) 700 minutes

b) When will the number of bacteria reach 5000

Answer 1

This is an example of exponential growth. The growth law for this problem is

p(t) = 620 (2)^t/0.5 = 620 (2)^2t,

where t is the elapsed time in hours (the 0.5 is the doubling period).

(a)(i)

Plug t=3 into the growth law and evaluate.

(a)(ii)

Convert 700 minutes to hours, and plug that into the growth law and evaluate.

(b)

Set p(t)=5000 and solve for t.

620 (2)^2t = 5000

log620 + 2t log2 = log5000

In hours,

t = (log5000 - log620) / (2 log2) = ?

Use any base for the logs, as long as you use the same base for both logs. You should be able to finish from here.