Name:Review sheet for exponential test
1. In the sequence -2, 6, -18, 54, what is the 12th term?
2. If the common ratio of a sequence is -2, and a1 is -4, then what is the 11th term?
3. You deposit $750 in an account with 7% interest compounded semiannually. What is the balance in the account after 4 years?
4. You deposit $1,200 in an account with 3.5% interest compounded quarterly. What is the balance in the account after 8 years?
5. The town manager reports that incoming revenues for a given year were $2 million. The budget director predicts that revenues will increase by 4% per year. How much revenue will the town have available 10 years from the date of the town manager’s report?
6. A fisheries manager determines that there are approximately 3000 bass in a lake. The population increases by 2% per year. About how long will it be before there are 4000 bass in the lake?
7. A business purchases a computer system for $2000. The tax code allows them to take off a portion of that purchase for each year the computer system is used. If the value of the system is depreciated at a rate of 15% per year. How much is the computer worth after 4 years?
8. A new truck has a value of $36,000. It depreciates in value 12% each year. To the nearest tenth of a year, when will the truck be worth half its original value?
9. The graph of an exponential function defined as f(x) = abx crosses the y-axis at (0, 4). The function is transformed to g(x) so that it crosses the y-axis at (0, 2). For g(x) = f(x) + k, what is the value of k?
10. Describe how the graph of f(x) = 5x would change if you were to graph
g(x) = 5x + 3.
11. If you have the parent function of f(x) = 2x translated so that the new function g(x) = f(x) + k has an asymptote of y = -5, what is the equation for g(x)? What is the y-intercept for g(x)?
For 12 – 15: Which type of function best models the data in each ordered pair? Write an equation to model the data.
12. (–1, 4), (0, 5), (1, 4), (2, 1), (3, –4)
13. (–2, –36), (–1, –12), (0, –4),
14. (0, –6), (4, –5), (6, –4.5), (8, –4), (12, –3)
15. (–1, –6), (0, –1), (2, –3), (3, –10), (4, –21)
16. For, the average rate of change of is 2.8, while for the average rate of change is 10.4. For when , the average rate of change is 4.5, and when the average rate of change is 4.5. Justify which function is linear and which is exponential by filling out the blanks below. (3 pts)
is ______because______
is ______because______
______
17. In the exponential function f(x) = 4,500(1.28)x, by what percentage does the value increase every year?
18. The base of a pile of wood has 200 pieces of wood in it The next layer has 194 pieces. The following row has 188 pieces of wood. If the pattern continues, in what row will there be 92 pieces of wood?
For 19 - 20 , Find which type of function each table best represents. (linear, quadratic or exponential). Give the r2 value and the equation.
19.
X / 1 / 2 / 3 / 4 / 5y / 4 / 6 / 6 / 4 / 1
20.
X / 0 / 1 / 2 / 3 / 4 / 5y / 49 / 76 / 102 / 127 / 150 / 174
21.
X / 0 / 1 / 2 / 3 / 4 / 5y / 1/3 / 2 / 4 / 9 / 26 / 80