Define Exponential Growth

Define Exponential Growth Exponential growth is a growth that occurs when rate of change increases at equal intervals. In simple words, any quantity that grows by a fixed percent at regular intervals. A best example of exponential growth is increasing human population. Exponential growth is represented by a function y= a (1 + r) x where a is the initial amount before measuring r is the rate or percent and x is the number of time interval passed. The following are the examples that explain exponential growth. Example 1: James started his bank account with $200 at an annual rate of 4%. Find the amount of money left in the account after 15 years. Solution : Given Initial amount (a) = $200 = Annual rate (r) = 4% = 4/100 = 0.04 = Number of years(x) = 15 = Substitute the given values in exponential growth formula, = y= a (1 + r) x = y = 200 (1 + 0.04) 15 = y = $ 360 = Amount of money left in his account after 15 years = $ 360. Example 2: Brandy has $600 in her account after 5 years of investing at rate of 2% every year. How much money did she started with? Solution 2: Given: Amount in her account = $600 = Annual rate (r) = 5% = 5/100 = 0.05 = Number of years(x) = 2 = Use Exponential growth formula, = y= a (1 + r) x = 600 = a (1 + 0.05)2 = 600 = a. 1.1025 = a = 544 = Initial amount she had was $544.