# Calculus

posted by .

An investment grows ar a rate of 2.5% each year compounded continuously. Approximately how long will it take the investment to double?

• Calculus -

dx/dt = .025 x
dx/x = .025 dt

ln x = .025 t + c

x = e^(.025 t+c) = e^c e^.025 t

so x = C e^.025 t
at t= 0, x = C e^0 = C
when is x = 2C ???
2C = C e^.025 x
e^.025 x = 2
.025 x = ln 2 = .6931
x = 27.7 years

## Similar Questions

1. ### Math

If \$8,500 is invested at 6% compounded continuously, how long will it take to double the investment?
2. ### math

How long will it take for an investment of \$13,000 to double if the investment earns interest at the rate of 6%/year compounded continuously?
3. ### math

Approximately how long will it take an investment of \$300 to triple, if the interest rate is 3.5% per year compounded continuously?
4. ### math

How long it will take for an investment of 1000 dollars to double in value if the interest rate is 9.5 percent per year, compounded continuously?
5. ### Math

How long it will take for an investment of 2000 dollars to double in value if the interest rate is 9.5 percent per year, compounded continuously?
6. ### How long will it take the investment to double?

\$3,600 is invested in an account at an annual interest rate of 4.8% compounded continuously. How long, to the nearest tenth of a year, will it take the investment to double in size?
7. ### math

1. You want to invest \$10,000 dollars. How long will it take to double your investment at an annual interest rate of 10%, compounded continuously?
8. ### Algebra 1

An investment grows according to the exponential equation y = 15,000 · 1.07x, where x is the number of years invested. Which of the following statements is true?
9. ### Algebra

An investment grows according to the exponential equation y = 15,000 · 1.07x, where x is the number of years invested. Which of the following statements is true?
10. ### Pre-Calc

An initial investment of \$9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?

More Similar Questions