karthikpandian19 wrote:A small town's population doubles every 5 years. Approximately how many years will it take for the population to grow from 100 to 25,000 people?
(A) 15 (B) 20 (C) 30 (D) 35 (E) 40
We could use the formula for exponential growth:
Final Amount = Original Amount * (Multiplier)^(Number of changes)
In the problem above:
Final Amount = 25,000
Original Amount = 100
Multiplier = 2 (since the population keeps doubling)
Number of changes = x.
Plugging these values into the formula, we get:
25,000 = 100 * 2^x
2^x = 250.
Since 2^8 = 256, x ≈ 8.
Since the number of changes = 8, and each change takes 5 years, the total number of years = 8*5 = 40.
The correct answer is
E.
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