write an exponential function to model the following situation.
a population of 140,000 grows 4% per year for 16 years.
how much will the population be after 16 years?
write an exponential function in terms of x
after 16 years, the population will be?
To model this situation with an exponential function, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount or population
P = initial amount or population
r = rate (expressed as a decimal)
n = number of times compounded per year
t = number of years
In this case, the initial population (P) is 140,000, the rate (r) is 0.04 (4% expressed as a decimal), the number of times compounded per year (n) is 1 (compounded annually), and the number of years (t) is 16.
Plugging these values into the formula, we get:
A = 140,000(1 + 0.04/1)^(1*16)
Simplifying further:
A = 140,000(1 + 0.04)^(16)
Calculating inside the parentheses:
A = 140,000(1.04)^(16)
Using a calculator to compute:
A ≈ 140,000 * 1.716135954
A ≈ 240,270.23
Therefore, after 16 years, the population will be approximately 240,270.23.