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.
y= __(__)^x
140,000 * 1.04 sixteen times which is
140,000 * 1.04^16
= 140,000 * 1.873 = 262,217.37
the 0.37 is a very small person
To write an exponential function that models this situation, we need to use the formula:
y = a * (1 + r)^x
Where:
- y is the final population after x years
- a is the initial population
- r is the growth rate (expressed as a decimal)
- x is the number of years
Given that the initial population (a) is 140,000 and the growth rate (r) is 4% or 0.04 per year, we can substitute these values into the equation:
y = 140,000 * (1 + 0.04)^x
Since we want to find the population after 16 years, we can replace x with 16:
y = 140,000 * (1 + 0.04)^16
Simplifying further will give us the exponential function in terms of x:
y = 140,000 * (1.04)^16