Answer:
It takes 1.77 hours for the population to double.
Step-by-step explanation:
Equation for population growth:
The equation for population growth, after t hours, with a growth rate parameter of r, as a decimal, is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
Growth rato parameter of 48% per hour
This means that [tex]r = 0.48[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = P(0)(1+0.48)^t[/tex]
[tex]P(t) = P(0)(1.48)^t[/tex]
How many hours does it take the size of the sample to double?
This is t for which P(t) = 2P(0). So
[tex]P(t) = P(0)(1.48)^t[/tex]
[tex]2P(0) = P(0)(1.48)^t[/tex]
[tex](1.48)^t = 2[/tex]
[tex]\log{(1.48)^t} = \log{2}[/tex]
[tex]t\log{1.48} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.48}}[/tex]
[tex]t = 1.77[/tex]
It takes 1.77 hours for the population to double.
