It will take 15 years for the population to quadruple
Step-by-step explanation:
The formula for continuously compounding rate is
, where
- A is the future amount
- P is the initial amount
- r is the interest as a decimal
- t is the time in years
Assume that the initial population is P
∵ The initial population = P
∵ The growth rate = 9% ⇒ compounded continuously
∴ r =
= 0.09
∵ The population will quadruple in t years
∴ A = 4P
- Substitute these values in the formula
∵ 
∴ 
- Divide both sides by P
∴ 
- Insert ㏑ to both sides
∴ ㏑(4) = ㏑(
)
∵ ㏑(
) = n
∴ ㏑ (4) = 0.09 t
- Divide both sides by 0.09
∴ t = 15.4
∴ t = 15 years to the nearest whole number
It will take 15 years for the population to quadruple
Learn more:
You can learn more about the logarithmic function in brainly.com/question/11921476
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