Question

the population of a certain city was 3178 in 2000. it is expected to decrease by about 0.46% per year. write an exponential decay function and use it to approximate the population in 2020

Answer 1

To approximate the population in 2020, we can use the exponential decay function P(t) = 3178 * e^(-0.0046t).

Substituting t = 20 into the function, we find that the population in 2020 is approximately 3104.

Step-by-step explanation:

To write an exponential decay function, we need to use the formula P(t) = P(0) * e^(kt), where P(t) is the population after t years, P(0) is the initial population, e is the base of the natural logarithm, and k is the rate of decay.

In this case, the initial population is 3178 and the decay rate is 0.46% or 0.0046.

So, the function becomes P(t) = 3178 * e^(-0.0046t).

To approximate the population in 2020, we can substitute t = 20 into the function.

Using a calculator, we find that

P(20) ≈ 3178 * e^(-0.0046*20)

≈ 3103.82.

Therefore, the population in 2020 is approximately 3104.