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,...

1. 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. 

1. Find the function that satisfies the equation, given that approximately 4.7 billion gallons of bottled water were sold in 2000.
2. b) Predict the number of gallons of water sold in 2025.
3. 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?