Question

3) A certain strain of bacteria will double its population every 2.4 hours, given enough food and room. Acolony's population, B, is calculated with the formula:B = P. (2)/2.4where P is the initial population, and t is the time (in hours) that it's allowed to grow.If a population of bacteria started with 1,000, how long would it take for this colony to reach a population of1,000,000, to the nearest hour?

Answer 1

B = P•(2)^t/2.4

Then now write

P= 1,000

B= 1,000,000

So therefore

B/P= 1000 = (2)^t/2.4

Now find t

t/2.4 = log2 1000

t/2.4= 9.96

Then

t = 2.4x9.96 = 23.9 , to nearest hour

Answer is

t = 24 hours