Before Class Begins: Math Background Assessment: Answer all multiple choice questions by the Friday before the beginning of the semester:
(1) Suppose some quantity is growing at a geometric rate of 3%/year. About how long will it take to grow by a factor of eight?
- 267 years
- None of the other answers
- 24 years
- 2.4 years
- 75 years
- There is not enough information to give an answer
(2) Suppose some quantity is converging to its steady-state value at a geometric rate of 5%/year. About how long will it take to close half the gap from its current value to its steady-state value?
- 20 years
- 14 years
- 25 years
- None of the other answers
- 10 years
- We do not have enough information to answer the question
(3) Suppose that total production is equal to a constant time the square root of the capital stock, and that the capital stock is growing at a geometric rate of 6%/year. How rapidly is total production growing?
- 5.5%/year
- 6%/year
- None of the other answers
- There is not enough information
- 3%/year
- 2.45%/year
(4) Suppose that production per worker is equal to a constant times the square root of the quantity that is the total capital stock divided by the number of workers. Suppose further that the total capital stock is growing at 6%/year and the number of workers is growing at 2%/year. How rapidly is production per worker growing?
- 4%/year
- There is not enough information
- 3%/year
- 2%/year
- 1.73%/year
(5) Suppose that we have a quantity x that follows the equation:
dx(t)/dt = -(0.08)x(t) + 0.32
What is the long-run steady-state asymptote to which x(t) will converge?
- None of the other answers
- 4
- 24
- 40
- There is not enough information
- 32
(6) What is dx(0)/dt--that is, the rate of change of x(t) at time 0?
- 0 per unit of time
- None of the others answers
- +0.64 per unit of time
- +0.32 per unit of time
- -0.32 per unit of time
- There is not enough information
Housekeeping:
