Question

The population of a small town is decreasing at a rate of 2.5% each year. If the current population of the town is 3500, write an exponential decay function to model this situation. How many people will live in the town after 15 years?

Options:
a) P(t) = 3500 ✕ (1 - 0.025)ᵗ
b) P(t) = 3500 ✕ (1 + 0.025)ᵗ
c) P(t) = 3500 ✕ (0.975)ᵗ
d) P(t) = 3500 ✕ (1.025)ᵗ

Answer 1

The exponential decay function for a town with population decreasing at a rate of 2.5% per year and current population of 3500 is P(t) = 3500 × (0.975)^t. After 15 years, the population will be approximately 2235 people.

Step-by-step explanation:

The exponential decay function that models the decreasing population of a small town at a rate of 2.5% each year when the current population is 3500 is given by the formula P(t) = 3500 × (0.975)^t. This is because each year the population retains 97.5% of its size from the previous year (which is 100% - 2.5% = 97.5%). To calculate the population after 15 years, we plug in t = 15 into the decay function: P(15) = 3500 × (0.975)^{15}.

Doing the calculation:

P(15) = 3500 × (0.975)^{15}

P(15) = 3500 × 0.638618

P(15) ≈ 2235

Therefore, after 15 years, roughly 2235 people will live in the town.