Question

a city doubles its size every 52 years. if the population is currently 637,100, what will the population be in 208 years?
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Explanation:

Step1: Find the number of doubling periods

To find how many times the population doubles in 208 years, divide 208 by 52.
$$\frac{208}{52} = 4$$
So there are 4 doubling periods.

Step2: Calculate the final population

The formula for exponential growth (doubling) is \( P = P_0 \times 2^n \), where \( P_0 \) is the initial population, \( n \) is the number of doubling periods.
Here, \( P_0 = 637100 \) and \( n = 4 \).
$$P = 637100 \times 2^4$$
$$2^4 = 16$$
$$P = 637100 \times 16 = 10193600$$

Answer:

10193600