Question

Rearrange the boxes below to represent a model for the following situation. The population of a city with an initial amount of 20000 people decreases yearly al a rate of 8% if P represents the population after t years.

Answer 1

After "t" years the population of the city is given by: "P(t) = 20000*(0.92)^t"

Explanation:

Since the population of this city decreases at a rate of 8%, then after the first year the population is:

P(1) = 20000*(1 - 8/100) = 20000*(0.92)

While after the second year it is:

P(2) = P(1)*(0.92) = 20000*(0.92)*(0.92) = 20000*(0.92)²

And after the third year:

P(3) = P(2)*(0.92) = 20000*(0.92)*(0.92)²= 20000*(0.92)³

And so on, therefore after "t" years, we have:

P(t) = 20000*(0.92)^t