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 = 79000.056t. When will the account be worth $12,365?

Answer 1

To find out when the account will be worth $12,365, we can set up the equation and solve for t in the exponential growth model:

A = 79000.056t

Given that A is the final amount we want to reach ($12,365), we can substitute it into the equation:

12365 = 79000.056t

Now we can solve for t. Divide both sides of the equation by 79000.006:

t = 12365 / 79000.056

Use a calculator

t ≈ 0.1566 years

To convert this to months, we multiply by 12:t ≈ 0.1566 * 12

t ≈ 1.8799 months

Therefore, the account will be worth $12,365 approximately 1.8799 months after the year 2000, assuming the exponential growth model A = 79000.056t.