Answer:
It takes 7.37 hours for the size of the sample to double.
Step-by-step explanation:
Continuous exponential growth model:
The continuous exponential growth model for populations is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate parameter, as a decimal.
Growth rate parameter of 9.4% per hour.
This means that [tex]r = 0.094[/tex]
So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(t) = P(0)e^{0.094t}[/tex]
How many hours does it take for the size of the sample to double?
This is t for which P(t) = 2P(0). So
[tex]P(t) = P(0)e^{0.094t}[/tex]
[tex]2P(0) = P(0)e^{0.094t}[/tex]
[tex]e^{0.094t} = 2[/tex]
[tex]\ln{e^{0.094t}} = \ln{2}[/tex]
[tex]0.094t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.094}[/tex]
[tex]t = 7.37[/tex]
It takes 7.37 hours for the size of the sample to double.
