Question

A town starts with 30,000 residents and grows at a continuous rate of 7% per year. (a) Write a formula for the population of the town after t years. NOTE: Enter the exact answer. Do not include commas P(t)= (b) What is the population of the town after 4 years? NOTE: Round your answer to the nearest person. Do not include commas. P= (c) Find the annual growth rate of the population of the town. NOTE: Round your answer to two decimal places.

Answer 1

The population growth of a town with a continuous rate of 7% per year would follow the formula P(t) = 30,000(1 + 0.07)^t. After 4 years, the population would grow to approximately 37,699 residents. The annual growth rate is 7%.

Step-by-step explanation:

This problem is a classic example of a compound interest problem, but with population growth. (a) The formula for the population after t years would be P(t) = P0(1 + r)^t, where P0 is the starting population (30,000), r is the growth rate (expressed as a decimal), and t is the time in years. In this case, this would be P(t) = 30,000(1 + 0.07)^t.

(b) The population after 4 years would be P(4) = 30,000(1 + 0.07)^4. Doing the calculation, the population after 4 years will be approximately 37,699 people.

(c) The annual growth rate of the town population, given as 7%, and in decimal form, it would be represented as 0.07.

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