Question

Jennifer starts a new investment account that grows exponentially. Given the initial investment of $50,000 growing at a rate of about 15% annually:

1. Determine a function, I(t), that determines Jennifer's investment account balance after t years. For the exponential growth function, what are the a and b values? What do those values represent?
a) I(t) = 50000(1 + 0.15)^t; a = 50000, b = 0.15; a represents the initial investment, and b represents the growth rate.
b) I(t) = 50000(0.15)^t; a = 50000, b = 0.15; a represents the initial investment, and b represents the growth rate.
c) I(t) = 50000(1 - 0.15)^t; a = 50000, b = -0.15; a represents the initial investment, and b represents the decrease rate.
d) I(t) = 50000(1 + 0.15)^t; a = 0.15, b = 50000; a represents the growth rate, and b represents the initial investment.

2. Calculate how much money Jennifer will have after 10 years.
a) Approximately $222,500
b) Approximately $172,000
c) Approximately $100,000
d) Approximately $250,000

3. What if Jennifer was able to deposit $100,000 as her initial investment instead of $50,000. Write a new function, N(t), to show this change. Calculate how much money Jennifer would have after 8 years.

Answer 1

The correct function to determine Jennifer's investment account balance is I(t) = 50000(1 + 0.15)^t. After 10 years, Jennifer will have approximately $222,500. If Jennifer had made an initial investment of $100,000 instead of $50,000, she would have approximately $201,536 after 8 years.

Step-by-step explanation:

The correct function to determine Jennifer's investment account balance after t years is:

I(t) = 50000(1 + 0.15)^t

The values for a and b in this function are:
a = 50000 (which represents the initial investment)
b = 0.15 (which represents the growth rate)

To calculate how much money Jennifer will have after 10 years, we can substitute t = 10 into the function:

I(10) = 50000(1 + 0.15)^10
I(10) = 50000(1.15)^10
I(10) ≈ $222,500

If Jennifer had made an initial investment of $100,000 instead of $50,000, the new function to determine her account balance after t years would be:

N(t) = 100000(1 + 0.15)^t

To calculate how much money Jennifer would have after 8 years with this new initial investment:

N(8) = 100000(1 + 0.15)^8
N(8) ≈ $201,536