Applications of Exponential Functions

Population Growth Population growth can be modeled by the basic form of the exponential function y = abx. Growth: b > 1 b = “growth factor” a = “initial amount” x = time y = ending amount

Population Growth In 2003, the population of the popular town of Smithville was estimated to be 35,000 people with an annual rate of increase (growth) of about 2.4%. What is the growth factor? After one year: 35,000 + (0.024)(35,000) Factor out 35,000 35,000(1 + 0.024) = 35,000(1.024) So, the growth factor is 1.024

Population Growth 2. Write an equation to model future population growth in Smithville. y = abx y = a(1.024)x So, y = 35,000(1.024)x, where x is the number of years since 2003.

Population Growth 3. Use the equation that you’ve written to estimate the population of Smithville in 2007 to the nearest one hundred people. y = 35,000(1.024)4 = 38,482.91 = 38,500

Compound Interest What is interest? Compound Interest: Interest that is earned on both the principal and any interest that has been earned previously. Balance: The sum of the Principal and the Interest

Compound Interest Formula: A: the ending amount P: the beginning amount (or "principal”) r: the interest rate (expressed as a decimal) n: the number of compoundings in a year t: the total number of years

Compound Interest Jackie deposits $325 in an account that pays 4.1% interest compounded annually. How much money will Jackie have in her account after 3 years? A = 325(1 + 0.041)1(3) 1 A = 325(1.041)3 A = $366.64 Jackie will have $366.64 in her account after 3 years.