Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 9.8% per hour. How many hours does it take for the size of the sample to double?
Do not round any intermediate computations, and round to the nearest hundredth.

Answer 1

Bacteria population increases by 9.8% per hour.
Population = (1.098)^hours
Solving this for time we get:

Time = log(ending amount / beginning amount) ÷ log (1 + rate)


Since we must solve the problem for the population to double, we'll say 
beginning amount = 100 and ending amount = 200
Time = log(200 / 100) ÷ log (1 + .098)

Time = log(2) ÷ log (1.098)
Time = 0.30102999566 / 0.040602340114
Time = 7.4141045766 Hours

Time = 7.41 Hours (rounded to nearest hundredth.

Source:
http://www.1728.org/expgrwth.htm