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 \( (1.05)^{612} \):
- Using a calculator, find \( (1.05)^{612} \).
Calculating this value gives approximately \( 5.123 \times 10^{13} \).
- Now, multiply by 250:
\[ P(612) \approx 250 \times 5.123 \times 10^{13} \approx 1.28075 \times 10^{16} \]
- 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.