# DOUBLING TIME GROWTH FORMULA

## Formula

If an initial population of size P doubles every d years (or any other unit of time), then the formula to find the final number A in t years is given by

A = P(2)t/d

## Solved Problems

Problem 1 :

The number of rabbits in a certain population doubles every 40 days. If the population starts with 12 rabbits, what will the population of rabbits be 160 days from now?

Solution :

Doubling-Time Growth Formula :

A = P(2)t/d

Substitute.

P = 12

t = 160

d = 40

Then,

A = 12(2)160/40

= 12(2)4

= 12(16)

= 192

So, the population of rabbits after 160 days from now will be 192.

Problem 2 :

The population of a western town doubles in size every 12 years. If the population of town is 8,000, what will the population be 18 years from now?

Solution :

Doubling-Time Growth Formula :

A = P(2)t/d

Substitute.

P = 8000

t = 18

d = 12

Then,

A = 8000(2)18/12

= 8000(2)1.5

Use a calculator.

22,627

So, the population after 18 years from now will be about 22,627.

## Related Topics

Exponential Growth and Decay

Half-Life Decay Formula

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