Number of bacteria in a certain population Increases according to a continuous exponential growth model with How many hours does it take the size of the sample to double ? growth rato parameter of 48% per hour

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 hourThis 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.