# Exponential Growth Formula

$y=a{(1+r)}^{x}$

a = initial amount

r = growth rate as a decimal

x = number of time intervals passed (days, months, years)

y = amount after x time

This formula is used to express a function of exponential growth.

Example 1:

In 2005, there were 180 inhabitants in a remote town. Population has increased by 12% every year. How many residents will there be in 10 years?

Step 1:

Identify the variables.

a = 180

r = 12% = .12

x = 10

y = ?

Step 2:

Substitute.

y = 180 (1 + .12)^{10}

y = 180 (1.12)^{10}

y = 559 rounded to the nearest person since we can't have part of a person

Answer:

After 10 years, there will be 559 people in that town.

Example 2 :

The number of subscribers to a new magazine has increased by 5% each month. In the first month, they had 2,250 subscribers. If the growth continues at this rate, how many subscribers can the magazine expect to have after 2 years?

Step 1:

Identify your variables.

a = 2250

r = 5% = .05

x = 24 since it increases by 5% each month, the time interval is months

y = ?

Step 2:

Substitute and solve for y.

y = 2250(1 + 0.05)^{24}

y = 2250(1.05)^{24}

y = 7,256

Answer:

There will be 7,256 subscribers after 2 years.

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