The population of Pinkville is 250. The function P(t)=250(1.05)t

Question

𝑃
(
𝑡
)
=
250
(
1.05
)
𝑡
represents what the future population of the town will be in t
𝑡
years. What will the population be in 612
6
1
2
years, to the nearest whole number? What is P(612

Answer 1

To find the population of Pinkville after 612 years using the population function \( P(t) = 250(1.05)^t \), we can substitute \( t = 612 \) into the equation.

\[ P(612) = 250(1.05)^{612} \]

Now, let's calculate \( (1.05)^{612} \):

1. Using a calculator, find \( (1.05)^{612} \).

Calculating this value gives approximately \( 5.123 \times 10^{13} \).

2. Now, multiply by 250:

\[ P(612) \approx 250 \times 5.123 \times 10^{13} \approx 1.28075 \times 10^{16} \]

3. Rounding to the nearest whole number, we have:

\[ P(612) \approx 12807500000000 \]

Thus, the population of Pinkville in 612 years would be approximately 12,807,500,000,000.