Question

a towns population is currently 100,000 people. the mayor discovered that the population is declining at a rate of 3% annually. if this rate continues, what will the population of the town be in 4 years? round your answer to the nearest whole number. 88,529 people 91,267 people 97,000 people 112,551 people

Explanation:

Step1: Define decay formula

Use exponential decay formula: $P(t) = P_0(1-r)^t$
Where $P_0=100000$, $r=0.03$, $t=4$

Step2: Substitute values into formula

$P(4) = 100000(1-0.03)^4$

Step3: Calculate the decay factor

$(0.97)^4 = 0.97\times0.97\times0.97\times0.97 = 0.88529281$

Step4: Compute final population

$P(4) = 100000\times0.88529281$

Answer:

88,529 people