Question 1067224: 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)
2. Calculate how much money Jennifer will have after 10 years. (10 points)
3. What is 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)
Calculate how much money Jennifer would have after 8 years. (2 points)
Using complete sentences, compare the differences in the functions and the amount of money after 8 years for the two different functions. (5 points)
4. Graph the function I(t) and identify the y-intercept and the equation of the asymptote. (5 pts)
5. Graph the function N(t) and identify the y-intercept and the equation of the asymptote. (5 pts)
6. What does the asymptote mean in terms of Jennifer’s investment account? Be sure to explain your reasoning for credit. (5 pt)
7. Due to a worldwide recession, Jennifer’s financial advisor informs her the account is no longer growing after 4 years. He recommends she move her money to an account that is more conservative and earns only 4% annually. Determine the amount in Jennifer’s investment account after 4 years(using the $50,000 investment), rounding to the nearest dollar. It may be helpful to create a table. (10 points)
8. Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation. (5 pts)
9. Did the asymptote of the new function change due to Jennifer moving her investment? Explain your reasoning. (5 pts)
Part II:
10. Determine the area of a rectangle whose length is expressed as 3x3y2 and the width is expressed as 5x2y4. (5 points)
11. Determine the volume for a prism whose length is expressed as 3x3y2 and the width is expressed as 5x2y4 and a height of 2xy2 (5 points)
Part III. Sequences
A national pool tournament starts with 650 teams. Each round sends half the teams to the losers bracket.
12. Complete the table below to show the number of teams in the tournament (5 points)
13. Write an explicit formula to describe this sequence that will determine how many teams are playing at any given round. Describe what “a” and “r” represent. (10 points)
15. How are linear and exponential functions similar and different. Discuss the relationship between the m and b in y= mx+b and the a and b or a and r in y = a (b)x or an = a1(r)x. (5 points)
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! 15,000(1+0.15)^t
I don't understand a and b values.
To find how much she has after 10 years, 8 years, or n years substitute the exponent t with the number you want and calculate.
Every other question: same, substitute the appropriate number with the number you want and calculate.
Good luck
John
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