Under ideal conditions a certain bacteria population is known to double every two hours.

Suppose there are initially 50 bacteria.


(a) What is the size of the population after 6 hours?
(b) What is the size of the population after t hours?

(c) What is the size of the population after 11 hours?
(d) Graph the population function and estimate the time for the population to reach 140,000. (Give your answer to the nearest hundredth.)

a) 50 X 2^(6/2) = 50 X 2^3 = 50 X 8 = 400
b) 50 X 2^(t/2)
c) 50 X 2^(11/2) = 50 X 2^5.5 = 50 X 45.254834 = 2,262.7417 (although I don't know what 0.7417 of a bacterium is)

d) time to reach 140,000:
Call the number of hours x. Then:
50 X 2^(x/2) = 140,000
2^(x/2) = 140,000 / 50
2^(x/2) = 2,800
(x/2) X ln(2) = ln(2,800)
(x/2) X 0.693415 = 7.937375
x / 2 = 7.937375 / 0.693415
x / 2 = 11.45
x = 2 X 11.45
x = 22.90 hours