A city's infrastructure improvement fund has $300,000 available, which is invested in an account with a 6.2% interest rate compounded continuously. How long will it take for the fund to grow to $600,000? 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 = 300,000 A = 600,000 r = 0.062Use formula and solve: Use the formula A = Pe^(rt) and solve for t. 600,000 = 300,000 * e^(0.062 * t)Divide and simplify: Divide both sides by 300,000. 2 = e^(0.062 * t)Take natural logarithm: Take the natural logarithm of both sides to solve for t. ln(2) = 0.062 * tDivide and solve: Divide both sides by 0.062. t = ln(2) / 0.062Calculate t: Calculate the value of t. t ≈ 11.18Round to nearest tenth: Round to the nearest tenth. t ≈ 11.2 years

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A city's infrastructure improvement fund has $\$300,000$ available, which is invested in an account with a $6.2\%$ interest rate compounded continuously. How long will it take for the fund to grow to $\$600,000$ $?$ $\newline$ 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.

View step-by-step help

Home

Math Problems

Algebra 2

Continuously compounded interest: word problems

Full solution

Q. A city's infrastructure improvement fund has

\$300,000

available, which is invested in an account with a

6.2\%

interest rate compounded continuously. How long will it take for the fund to grow to

\$600,000

?

\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 $t$ . $P = 300,000$ $A = 600,000$ $r = 0.062$
Use formula and solve: Use the formula $A = Pe^{rt}$ and solve for $t$ . $600,000 = 300,000 imes e^{0.062 imes t}$
Divide and simplify: Divide both sides by $300,000$ . $2 = e^{0.062 imes t}$
Take natural logarithm: Take the natural logarithm of both sides to solve for $t$ . $\ln(2) = 0.062 \cdot t$
Divide and solve: Divide both sides by $0.062$ . $t = \ln(2) / 0.062$
Calculate $t$ : Calculate the value of $t$ . $t \approx 11.18$
Round to nearest tenth: Round to the nearest tenth. $t \approx 11.2$ years