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a city has a population of $370,000$ people. suppose that each year the population grows by $6\%$ . what will the population be after $11$ years?

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Exponential growth and decay: word problems

Full solution

Q. a city has a population of

370,000

people. suppose that each year the population grows by

6\%

. what will the population be after

11

years?

Recognize Compound Interest Formula: First, we need to recognize that the population growth each year is compound interest, so we use the formula for compound interest which is $P(1 + r)^n$ , where $P$ is the initial amount, $r$ is the rate of growth, and $n$ is the number of years.
Plug in Values: Now, let's plug in the values: $P = 370,000$ , $r = 6\%$ or $0.06$ , and $n = 11$ years.
Calculate Exponential Term: So the equation becomes $370,000(1 + 0.06)^{11}.$
Multiply to Find Population: Now calculate $(1 + 0.06)^{11}$ using a calculator. $\newline$ $(1 + 0.06)^{11} = 1.06^{11} \approx 2.012196$ .
Multiply to Find Population: Now calculate $(1 + 0.06)^{11}$ using a calculator. $(1 + 0.06)^{11} = 1.06^{11} \approx 2.012196$ .Next, multiply $370,000$ by $2.012196$ to find the population after $11$ years. $370,000 \times 2.012196 \approx 744,112.52$ .

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