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Answer :
The initial population of the town is 35.8 people.
The town's population is modeled by an exponential function P = f(t) = 35.8(1.025)^t, where:
P represents the population of the town in thousands at year t.
1.025 is the growth factor, which is greater than 1. This indicates an exponential growth. In words: The town's population is growing exponentially. Each year, the population increases by a factor of 1.025, which is a 2.5% increase compared to the previous year.
- Initial Population:
To find the initial population, we need to evaluate the function at t = 0 (year 0):
- P(0) = 35.8 * (1.025)⁰
Since any number raised to the power 0 equals 1, the initial population is:
P(0) = 35.8 * 1 = 35.8 (thousands).
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