Exponentials: Application 1

Exponentials

Write an equation to model a population that starts at 100,000 and grows 3.5% per year.

Step 1. Determine the initial value. The population starts at 100,000.

a = 100000

Step 2. Write the rate as a growth factor. The population is growing by 3.5%, add this to 100%. 100% + 3.5% = 103.5%, translated to a decimal 1.035

b = 1.035

Step 3. Write the equation.

y = a . b^x

y = 100000(1.035)^x