The value of a particular investment follows a pattern of exponential growth. You invested money in a money market account. The value of your investment t years after your initial investment is given by the exponential growth model A = 7300e0.066t. How much did you initially invest in the account?
e^0 = 1
so at time t=0, A = 7300
To find out how much you initially invested in the account, we can use the given exponential growth model.
The exponential growth model is represented by:
A = P * e^(rt)
Where:
A is the final value of the investment
P is the initial investment
e is the base of natural logarithms (approximately 2.71828)
r is the growth rate
t is the time in years
In this case, the formula for the investment is given as:
A = 7300e^(0.066t)
Since we want to find the initial investment, which is represented by P, we need to rearrange the formula to solve for P.
Divide both sides of the equation by e^(0.066t):
A/e^(0.066t) = P
Now, substitute the given values into the equation. We know that A = 7300 and t = 0 (since it's the initial investment).
P = 7300 / e^(0.066 * 0)
Since anything raised to the power of 0 equals 1, we have:
P = 7300 / e^0
e^0 = 1
Therefore, the initial investment (P) is equal to:
P = 7300 / 1
So, you initially invested $7300 in the account.