Question

The population of Leave Town is 123,000 and is decreasing at a rate of 2.375% each year. What is the exponential decay function to model this situation?

Options:
a) P(t) = 123,000 ✕ (1 - 0.02375)ᵗ
b) P(t) = 123,000 ✕ (1 + 0.02375)ᵗ
c) P(t) = 123,000 ✕ (0.97625)ᵗ
d) P(t) = 123,000 ✕ (1.02375)ᵗ

Answer 1

The exponential decay function that models the declining population of Leave Town at a rate of 2.375% per year is P(t) = 123,000 × (0.97625)ⁿ, where t is the number of years.

Step-by-step explanation:

The situation described involves a population that is decreasing annually at a specific rate, and the question asks for the exponential decay function to model this situation. The correct option to represent the population of Leave Town declining at a rate of 2.375% per year is given by the formula:

P(t) = 123,000 × (0.97625)ⁿ

The rate of decrease is 2.375%, which means the population retains 100% - 2.375% = 97.625% of its size each year. Therefore, the decay factor is 0.97625, and to find the population at time t, we raise this factor to the power of t and multiply by the initial population. Hence, the correct exponential decay function is option (c).