Question

the initial population was 50 thousand people and the population increased by 12% each year. Determine the function rule for this definition.

Answer 1

Answer:
`P(x) = 50,000(1.12)^x`

Step-by-step explanation: Let
`P(x)` be the population after x years. Since 50,000 is the initial population, P(0) = 50,000. Moreover, since the population increases 12% per year,


`P(x) = P(x - 1) + 12\% (P(x - 1)) \\ = P(x - 1) + 0.12(P(x - 1)) \\ \boxed{P(x) = 1.12(P(x - 1))}`

Using the preceding equation:


`P(1) = 1.12(P(0)) = 50,000(1.12) \\ P(2) = 1.12(P(1)) = 1.12(50,000(1.12)) = 50,000(1.12)^2 \\ P(3) = 1.12(P(2)) = 1.12(50,000(1.12)^2) = 50,000(1.12)^3 \\. \\. \\. \\P(x) = 1.12(P(x-1)) = 1.12(50,000(1.12)^(x-1)) = 50,000(1.12)^x \\\boxed{P(x) = 50,000(1.12)^x}`