Question 1068156: Jennifer starts a new investment account that grows exponentially. Her financial advisor tells her the initial investment of $50,000 grows 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? (5 points for the explanation of “a” and “b” and 5 points for the function)
answer:15000*(1+0.15)t
2. Calculate how much money Jennifer will have after 10 years. (10 points)
answer:$60683.366036
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. (3 points)
answer:100000*(1+0.15)t
Calculate how much money Jennifer would have after 8 years. (2 points)
answer:$305902.286254
Using complete sentences, compare the differences in the functions and the amount of money after 8 years for the two different functions. (5 points)
answer:??
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! y=ab^x, where a here is the amount deposited, and x is the number of compoundings.
I'd round to two decimal places, since it is money.
The figures are correct.
The second is more than the first because more was deposited.
The tripling time of money in years is ln3/interest rate as decimal number, because p/po=e^rt and ln (3), which is the ratio=rt, so ln3/r=t
here in 10 years ln3/.15=7.32 years so that tripling just occurs for the second, but the first has quadrupled.
Quadrupling is doubling of doubling, and the rule of 70 is used there, where 70 over the rate (in per cent) is the doubling time--70/15=4.67 years, so this doubled and again doubled. That is consistent with $60,000.
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