Question

question
a town has a population of 5000 and grows at 4% every year. what will be the population after 7 years, to the nearest whole number?
answer attempt 1 out of 2
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Explanation:

Step1: Define exponential growth formula

The exponential growth formula is $P(t) = P_0(1 + r)^t$, where $P_0$ is initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Identify given values

$P_0 = 5000$, $r = 0.04$, $t = 7$

Step3: Substitute values into formula

$P(7) = 5000(1 + 0.04)^7$

Step4: Calculate growth factor first

$(1.04)^7 \approx 1.315931779$

Step5: Compute final population

$P(7) = 5000 \times 1.315931779 \approx 6579.66$

Step6: Round to nearest whole number

Round $6579.66$ to the nearest integer.

Answer:

6580