Question

The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the population to quadruple according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.

Answer 1

It will take 15 years for the population to quadruple

Step-by-step explanation:

The formula for continuously compounding rate is  $A=Pe^{rt}$ , 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 = $\frac{9}{100}$ = 0.09

∵ The population will quadruple in t years

∴ A = 4P

- Substitute these values in the formula

∵ $A=Pe^{rt}$

∴ $4P=Pe^{(0.09)t}$

- Divide both sides by P

∴ $4=e^{0.09t}$

- Insert ㏑ to both sides

∴ ㏑(4) = ㏑( $e^{0.09t}$ )

∵ ㏑( $e^{n}$ ) = 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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