Explanation:
1. The function that determines Jennifer's investment account balance after f years is:
I(t) = ab^t
where a = $50,000 is the initial investment, b = 1.15 is the annual growth rate in decimal form, and t is the number of years.
The value of "a" represents the initial value of the investment, or the y-intercept of the exponential growth function. The value of "b" represents the growth factor, or the base of the exponential function, and it is the factor by which the investment grows each year.
2. To calculate how much money Jennifer will have after 10 years, we simply plug in t = 10 into the exponential growth function:
I(10) = ab^10 = $50,000 x 1.15^10 = $199,025.56
Therefore, Jennifer will have $199,025.56 in her investment account after 10 years.
3. The new function to show the change in Jennifer's investment if she invests $100,000 is:
N(t) = ab^t
where a = $100,000 is the initial investment, b = 1.15 is the annual growth rate in decimal form, and t is the number of years.
To calculate how much money Jennifer will have after 8 years, we simply plug in t = 8 into the exponential growth function:
N(8) = ab^8 = $100,000 x 1.15^8 = $239,869.58
Therefore, Jennifer will have $239,869.58 in her investment account after 8 years.
The difference between Jennifer's investment with an initial deposit of $50,000 and $100,000 is that the latter has a higher initial value or y-intercept of the exponential growth function. As a result, if the time frame and annual growth rate are the same, Jennifer's investment with $100,000 will have a larger value as compared to the investment with a $50,000 initial deposit.