The population of a small Midwestern town is 4500 The population is decreasing at a rate of 1.5% per year. Write an exponential decay function to model this situation. Then find the number of people in the town after 25 years.
y=(3/2)^x
You probably mean well, but some of your answers, like the one above, are incorrect.
Make sure you are familiar with the topic before you answer.
decrease of 1.5% ---> 98.5% or .985
Population = 4500(.985)^t, where t is the number of years
so when t = 25
population = 4500(.985)^25
= 3084
to the nearest whole number, can't have partial people
To model the population decrease in a small Midwestern town, we can use an exponential decay function. The general form of an exponential decay function is:
P(t) = P₀ * (1 - r)^t
where:
P(t) is the population at time t,
P₀ is the initial population,
r is the decay rate (expressed as a decimal),
t is the time in years.
Given that the initial population is 4500 and the decay rate is 1.5%, we first need to convert the rate to a decimal by dividing it by 100:
r = 1.5% / 100 = 0.015
So the exponential decay function for this situation is:
P(t) = 4500 * (1 - 0.015)^t
To find the number of people in the town after 25 years (t = 25), we substitute t = 25 into the equation:
P(25) = 4500 * (1 - 0.015)^25
Now we can calculate the value using a calculator or by simplifying the equation further:
P(25) ≈ 4500 * (0.985)^25
P(25) ≈ 4500 * 0.710
P(25) ≈ 3195
Therefore, after 25 years, the estimated number of people in the town is approximately 3195.
To model the population decrease in the small Midwestern town, we can use an exponential decay function. The general form of an exponential decay function is:
P(t) = P₀ * (1 - r)^t
Where:
- P(t) is the population at time t
- P₀ is the initial population
- r is the decay rate (as a decimal)
- t is the time in years
In this case, the initial population is 4500, and the rate of decrease is 1.5% per year, which can be written as 0.015.
Therefore, the exponential decay function for this situation can be written as:
P(t) = 4500 * (1 - 0.015)^t
To find the number of people in the town after 25 years, we can substitute t = 25 into the equation and calculate:
P(25) = 4500 * (1 - 0.015)^25
P(25) ≈ 4500 * (0.985)^25
Using a calculator, we can evaluate this expression:
P(25) ≈ 4500 * 0.715
P(25) ≈ 3217.5
Therefore, after 25 years, the estimated population of the small Midwestern town would be approximately 3217 people.