Question

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a city has a population of 290,000 people. suppose that each year the population grows by 6.75%. what will the population be after 13 years?
use the calculator provided and round your answer to the nearest whole number
people
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Explanation:

Step1: Define growth formula

This is exponential growth, use the formula:
$$P(t) = P_0(1 + r)^t$$
where $P_0=290000$, $r=0.0675$, $t=13$.

Step2: Substitute values

$$P(13) = 290000 \times (1 + 0.0675)^{13}$$

Step3: Calculate growth factor

First compute $(1.0675)^{13} \approx 2.3678$

Step4: Compute final population

$$290000 \times 2.3678 \approx 686662$$

Answer:

686662 people