Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 2.5% per hour. how many hours does it take for the size of the sample to double? note: this is a continuous exponential growth model. do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

Continuous exponential growth formula is given by:
A=Pe^(rt)
where A is the current amount
P=initial amount
r=rate
t=time

the time taken for the sample to double will be found as follows:
let:
P=x
A=2x
r=0.025
thus
2x=xe^(0.025t)
2=e^0.025t
introducing natural logs we get:
ln 2=0.025t
t=ln2/0.025
t=27.73 hours