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Math 1090-002 Practice Test 3 Spring 2013 Instructor:Jie Ma 1. For each function, find its inverse function, if possible. x3 −5 (a) f (x) = 3 x +1 q x+2 (b) f (x)= 2 4x−3 +1 2. Solve the following equations. (a) log2 (3x − 2) − log2 (x2 ) = 0 2 +x (b) 114 = 121x (c) log(x2 ) + 1 = log(3x + 1) (d) 3e2x − 30 = 9ex 3. Graph the following functions: (a) f (x) = 2x−1 + 3 (b) f (x) = log2 (x + 2) − 2 4. Find the 7th term of the sequence. Also calculate the sum of the first 20 terms for each sequence (You don’t have to simplify your answer for the sums). (a) Assume that the sequence is an arithmetic sequence. a2 = 2,a8 = 16 (b) Assume that the sequence is a geometric sequence. a2 = 2,a4 = 18 1 5. The Bryan Landscaping company earned $10, 000 in its first year of business which it deposited in a cd account earning 6% compounded daily for four years. What is the value of this account after the four year period? 6. Barney is saving for college. He is 10 years old and plans to go to college when he’s 18. He saves his allowance, $300 a month. He has the family butler deposit this into an annuity at 8% interest compounded monthly. How much will Barney have in his college account when he’s 18? 7. Larry’s daughter, Jeri, is engaged and will get married in three years. She wants a large, expensive wedding that will cost about $25, 000. In order to save for the wedding, Larry has found a relatively safe investment that pays 9% compounded monthly. What monthly payment must he make to this account in order to pay for Jeri’s wedding? 8. Amelia just inherited $250, 000 as a death benefit from her mother’s life insurance. She has deposited this amount in a savings account that pays 10% interest compounded monthly. How much can Amelia withdraw monthly if she intends to access this account for the next 20 years? 9. You find a bargain house which sells for $133, 000. (a) What are your monthly payments for a 30-year loan at 3.75% interest compounded monthly? (b) What is the total finance charge (interest) for this 30-year loan? 2