Question

a citys population is currently 467,500. if the population doubles every 42 years, what will the population be 168 years from now? people

Explanation:

Step1: Find the number of doubling periods

To find how many times the population doubles in 168 years, we divide the total time by the time it takes to double once. So, the number of doubling periods \( n=\frac{168}{42} \).
\( n = 4 \)

Step2: Calculate the future population

The formula for exponential growth (in this case, doubling) is \( P = P_0\times2^n \), where \( P_0 \) is the initial population, \( n \) is the number of doubling periods. Here, \( P_0 = 467500 \) and \( n = 4 \).
So, \( P=467500\times2^4 \)
First, calculate \( 2^4 = 16 \)
Then, \( P = 467500\times16 \)
\( P = 7480000 \)

Answer:

7480000