# Define Exponential Growth

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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)

=> 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.