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