A non-profit organization received a donation of $75,000 and decided to invest it in an account with a 4.8% interest rate compounded continuously to build a reserve fund. How long will it take for the donation to grow to $150,000? Round your answer to the nearest tenth. Use the formula A = Pe^rt, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.

Identify values: Identify the values for P, A, r, and t. P = 75000 A = 150000 r = 0.048 t = ?Use formula: Use the formula A = Pe^(rt). 150000 = 75000 * e^(0.048 * t)Divide sides: Divide both sides by 75000. 2 = e^(0.048 * t)Take ln: Take the natural logarithm (ln) of both sides. ln(2) = 0.048 * tSolve for t: Solve for t. t = ln(2) / 0.048Calculate value: Calculate the value of t. t ≈ 0.693147 / 0.048 t ≈ 14.4405625Round to tenth: Round to the nearest tenth. t ≈ 14.4 years

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A non-profit organization received a donation of $\$75,000$ and decided to invest it in an account with a $4.8\%$ interest rate compounded continuously to build a reserve fund. How long will it take for the donation to grow to $\$150,000$ $?$ $\newline$ Use the formula $A = Pe^{rt}$ , where $A$ is the balance (final amount), $P$ is the principal (starting amount), $e$ is the base of natural logarithms $(\approx 2.71828)$ , $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. $\newline$ Round your answer to the nearest tenth.

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Algebra 2

Continuously compounded interest: word problems

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Q. A non-profit organization received a donation of

\$75,000

and decided to invest it in an account with a

4.8\%

interest rate compounded continuously to build a reserve fund. How long will it take for the donation to grow to

\$150,000

?

\newline

Use the formula

A = Pe^{rt}

, where

A

is the balance (final amount),

P

is the principal (starting amount),

e

is the base of natural logarithms

(\approx 2.71828)

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\newline

Round your answer to the nearest tenth.

Identify values: Identify the values for $P$ , $A$ , $r$ , and $t$ . $P = 75000$ $A = 150000$ $r = 0.048$ $t = ?$
Use formula: Use the formula $A = Pe^{rt}$ . $150000 = 75000 imes e^{0.048 imes t}$
Divide sides: Divide both sides by $75000$ . $2 = e^{0.048 imes t}$
Take ln: Take the natural logarithm (ln) of both sides. $\ln(2) = 0.048 \cdot t$
Solve for $t$ : Solve for $t$ . $t = \frac{\ln(2)}{0.048}$
Calculate value: Calculate the value of $t$ . $t \approx \frac{0.693147}{0.048}$ $t \approx 14.4405625$
Round to tenth: Round to the nearest tenth. $t \approx 14.4$ years