Write an exponential function to model the following situation.
A population of 140,000 grows 3% per year for 15 years.
How much will the population be after 15 years?
Write an exponential function in terms of x.
After 15 years, the population will be?
To model this situation, we can use the formula for exponential growth:
P = P₀(1 + r)^t
Where:
P = final population after t years
P₀ = initial population
r = growth rate per year
t = number of years
In this case, the initial population (P₀) is 140,000, the growth rate (r) is 3% (or 0.03), and we want to find the population after 15 years (t = 15).
Plugging these values into the formula, we get:
P = 140,000(1 + 0.03)^15
Simplifying and calculating, we find:
P ≈ 236,578.75
Therefore, after 15 years, the population will be approximately 236,579.