## The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population

Question

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.) P0 = 5937.8 What will be the population in 10 years? (Round your answer to the nearest person.) 23751 persons How fast is the population growing at t = 10? (Round your answer to the nearest person.) 3293 persons/year

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2 months 2021-10-13T09:24:22+00:00 1 Answer 0 views 0

P0 = 5937.8 people

P(t = 10) = 23751 people

P'(t = 10) = 3293 persons/year

Step-by-step explanation:

Let the population has the formula of

Where P0 is the initial population at t = 0 and k is the constant that we are looking fore.

Since the population doubled after t = 5 years

So after t = 3 years, population is P = 9000:

After 10 years, population would be quadtripled (10 years is 2 times of 5 years):

The rate of change in population is the derivative of the population function with respect to t

So after t = 10 years the rate of change in population would be