Question

The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment, t years after 2000, is given by the exponential growth model A=4550e^0.065t.

A. How much did you initially invest in the account?
B. What is the interest rate?
C. In which year (2010, 2011, 2012, 2013) will the account be worth approximately $9301?

Answer 1

The initial investment was $4550, the interest rate is 6.5% per year, and the investment will reach approximately $9301 in the year 2010.

Step-by-step explanation:

The exponential growth model provided for the value of the investment is A=4550e^0.065t, where A is the amount after t years, 4550 is the initial investment, and 0.065 is the interest rate.

Part A: Initial Investment

To find the initial investment, we look at the value of the investment at t=0.

Plugging in t=0 into the model gives us

A=4550e^0, which simplifies to

A=4550 as e^0 is 1. Therefore, the initial investment was $4550.

Part B: Interest Rate

The interest rate given in the model is the exponent's coefficient, which is 0.065, or 6.5% per year.

Part C: Future Value of the Investment

To find in which year the account will be worth approximately $9301, we need to solve for t in the equation 4550e^0.065t = 9301. By taking natural logs on both sides and solving for t, we find that t is approximately 10 years. Hence, the investment will be worth approximately $9301 in the year 2010.