Question

a city’s population is currently 67,180. if the population doubles every 98 years, what will the population be 392 years from now? people

Explanation:

Step1: Find the number of doubling periods

To find how many times the population doubles in 392 years, we divide the total time by the doubling time. The doubling time is 98 years, so the number of periods \( n \) is \( n=\frac{392}{98} \).
\( n = 4 \)

Step2: Calculate the final population

The formula for exponential growth with doubling time is \( P = P_0\times2^n \), where \( P_0 \) is the initial population, \( n \) is the number of doubling periods. Here, \( P_0 = 67180 \) and \( n = 4 \).
So \( P=67180\times2^4 \)
First, calculate \( 2^4=16 \)
Then, \( P = 67180\times16 \)
\( P=1074880 \)

Answer:

1074880