In 2000,the population of Arizona was 5 million and growing continuously at a rate of 3.1% per year. Write a function f that models Arizona's population in millions x years after 2000.
F(x) = Po + Po*r*x,
Factor out Po:
F(x) = Po(1 + r*x),
F(x) = 5(1 + 0.031x)
To write a function that models Arizona's population in millions x years after 2000, we can use the formula for exponential growth:
f(x) = P * (1 + r)^x
Where:
- f(x) represents the population in millions x years after 2000
- P is the initial population in millions (in this case, 5 million)
- r is the growth rate per year (in this case, 3.1% or 0.031)
- x is the number of years after 2000
Now we can substitute the given values into the formula:
f(x) = 5 * (1 + 0.031)^x
Simplifying further:
f(x) = 5 * (1.031)^x
This is the required function that models Arizona's population in millions x years after 2000.