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# Compound interest. Suppose that P 0 is invested in the Mandelbrot Bond Fund for which interest is compounded continuously at 5.9% per year. That is,...

**Compound interest.**Suppose that P0 is invested in the Mandelbrot Bond Fund for which interest is compounded continuously at 5.9% per year. That is, the balance P grows at the rate given by

dP/dt = 0.059P

Find the function that satisfies the equation. Write it in terms of P0 and 0.059.

Suppose that $1000 is invested. What is the balance after 1 yr? After 2 yr?

When will an investment of $1000 double itself?

**2.Bottled water sales. **Since 2000, sales of bottled water

have increased at the rate of approximately 9.3% per year. That is, the volume of bottled water sold, G, in billions of gallons, t years after 2000 is growing at the rate given by

dG/dt = 0.093G.

- Find the function that satisfies the equation, given that approximately 4.7 billion gallons of bottled water were sold in 2000.
**b)**Predict the number of gallons of water sold in 2025.**c)**WhatisthedoublingtimeforG(t)?

**3.Annual interest rate. **Euler Bank advertises that it com- pounds interest continuously and that it will double your money in 15 yr. What is its annual interest rate?

**4. Oil demand. **The growth rate of the demand for oil in the United States is 10% per year. When will the demand be double that of 2006?