1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and then increased by 12.5% for the next 5 years. AT the end of 10 years, what was the value of each person's investment?
2. Investigate the following functions for both horizontal and vertical asymptotes, x and y-intercepts, and state the domain and range of each and where the function is increasing and decreasing.
(A) f(x) = (2x3 - 3x - 5)/(x3 - 8). (B) g(x) = (x - 3)/(x2 - 5x + 6)
3. A manufacturing company wants to package its product in a rectangular box with a square base and a volume of 32 cubic inches. The cost of the material used for the top is $.05 square inch; the cost of the material used for the bottom is $.15 per square inch, and the cost of the material used for four sides is $.10 per square inch. What are the dimensions of the box with the minimum cost?
4. In planning a restaurant, it is estimated that a revenue of $6 per seat will be realized if the number of seats is at most 50. On the other hand, the revenue on each seat will decrease by $.10 for each seat exceeding 50 seats. Find the revenue function where x = the number of seats exceeding 50 seats. What is the maximum revenue and what number of seats generates that maximum revenue.
5. You invest $1,000 at an annual interest rate of 5% compounded continuously. How much is your balance after 8.5 years? How long will it take you to accrue a balance of $4,000? What interest rate is required to yield a balance of $7,000 after 7 years?
6. A sum of $2,500 is deposited in a bank account that pays 5.25% interest compounded weekly. How long will it take for the deposit to double? How long will it take you to accrue a balance of $7,500? What interest rate is required to yield a balance of $7,000 after 7 years?
7. Solve the following logarithmic equations. A) log(x-1) - log(x+1) = 1; B) ln(x) = -1.147; C) ln(x) = (2/3)ln(8) + (1/2)ln(9) - ln(6); D) log5 (x) + log5 (x-4) = log5 (21); E) log4 (3x) - log4 (x2-1) = log4 (2)
8. Solve the following exponential equations. A) 3(7x+1) = 3(4x-5); B) 8x = 2(x-6); C) 3(x+2) = 5: D) 4(x) = 2(3x+4); E) e(x - 6) = 3.5.
9. Graph f(x) = 2x - 3 and approximate the zero of f to the nearest tenth. Also find the y-intercept and any horizontal and vertical asymptotes.
10. In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After 2 days there are 100 flies, and after 4 days there are 300 flies. How many flies will there be after 5 days?16. Differentiate the following functions using the limit definition:
Part A. f(x) = x2+x-5; Part B. f(x) = (4x+100); Part C. f(x) = 3/(x+4)
11. Find the following limits.
A
Part A denominator should be (x2 - 4) not (x2-4)