A strain of bacteria grows exponentially

Question

A strain of bacteria grows exponentially. Immediately after 2 hours there were 1000 bacteria, and immediately after three hours there were 5000 bacteria. If no bacteria die, then the time it takes for the population to double is?

Answer 1

We know that in one hour the population increased from 1000 to 5000.

 

1000 • 2^kt = 5000,  where t=1

2^k = 5000 / 1000 = 5

k • ln(2) = ln(5)

k = ln(5) / ln(2) = 2.3219

 

Growth equation

P = A • 2^2.32t

The population doubles when kt = 1

2.3219t = 1

t = 0.4306 hours = 25.84 minutes = 25:50.4 minutes:seconds