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natali 33 [55]
3 years ago
12

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
Mathematics
1 answer:
vladimir1956 [14]3 years ago
3 0

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:

P(t) = P(0)(1+r)^t

Growth rato parameter of 48% per hour

This means that r = 0.48. So

P(t) = P(0)(1+r)^t

P(t) = P(0)(1+0.48)^t

P(t) = P(0)(1.48)^t

How many hours does it take the size of the sample to double?

This is t for which P(t) = 2P(0). So

P(t) = P(0)(1.48)^t

2P(0) = P(0)(1.48)^t

(1.48)^t = 2

\log{(1.48)^t} = \log{2}

t\log{1.48} = \log{2}

t = \frac{\log{2}}{\log{1.48}}

t = 1.77

It takes 1.77 hours for the population to double.

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