It will take 15 years for the population to quadruple
Step-by-step explanation:
The formula for continuously compounding rate is [tex]A=Pe^{rt}[/tex] , where
Assume that the initial population is P
∵ The initial population = P
∵ The growth rate = 9% ⇒ compounded continuously
∴ r = [tex]\frac{9}{100}[/tex] = 0.09
∵ The population will quadruple in t years
∴ A = 4P
- Substitute these values in the formula
∵ [tex]A=Pe^{rt}[/tex]
∴ [tex]4P=Pe^{(0.09)t}[/tex]
- Divide both sides by P
∴ [tex]4=e^{0.09t}[/tex]
- Insert ㏑ to both sides
∴ ㏑(4) = ㏑( [tex]e^{0.09t}[/tex] )
∵ ㏑( [tex]e^{n}[/tex] ) = 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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