Question
Asked Nov 13, 2019
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The rate of growth dP/dt of a population of bacteria is proportional to the square root of t where P is the population size and t is the time in days (0 ≤ t ≤ 10). That is, dP/dt = k√t The initial size of the population is 300. After 1 day the population has grown to 800. Estimate the population after 8 days.

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Expert Answer

Step 1

The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days.

Step 2

Consider the rate at which the population of bacteria grow.

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dp ki dt Here, P is the population of bacteria and t is time taken by the bacteria to grow

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Step 3

Integrate the growth to find the population...

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dp fkVidt dt P k C 2 2 kt2 C 3

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Tagged in

Math

Calculus