Exponential Growth Formula
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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