Question

The population of a rural city follows the exponential growth model P(t) = 3100 e⁰.⁰³⁶ᵗ where t is the number of years after 1989.

a) What was the population of this city in 1989?

Answer 1

To find the population of the city in 1989 using the formula P(t) = 3100 e⁰.⁰³⁶ᵗ, we evaluate P(0) which yields 3100. This indicates that the population of the city in 1989 was 3100 residents.

Step-by-step explanation:

The question asks about the initial population of a rural city in 1989 based on the given exponential growth model P(t) = 3100 e⁰.⁰³⁶ᵗ, where t is the number of years after 1989. To find the population in 1989, we need to evaluate the function P(t) at t = 0.

To calculate this, we substitute t = 0 into the function:

• P(0) = 3100 e⁰.⁰³⁶·⁰
• P(0) = 3100 e⁰ (since any number raised to the power of 0 is 1)
• P(0) = 3100 (as e⁰ = 1)

Therefore, the population of the city in 1989 was 3100 residents.