Sample Midterm 2 WI 06

# A find the domain of f 4 points b find f 2 f 2 and f

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(a) Find the Domain of f. (4 points) (b) Find f ( - 2) , f (2), and f (4). (6 points) (c) Plot and Label the points you found in (b) and sketch a graph of y = f ( x ) . (5 points) x y

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Form A Page 4 of 7 4. Frank invested a total of \$7,000 in two different accounts. He put \$4,000 in an account which pays 5% interest, compounded monthly; and, he put the remaining \$3,000 in a second account which pays 4.1% interest, compounded continuously. Compute the total interest Frank earned at the end of 2 years. (Give your answer to the nearest cent .) (14 points)
Form A Page 5 of 7 5. (a) Solve the equation: 2 ln( x ) = ln(20 - x ) (8 points) (b) Using my calculator, I found the solution to the equation e 1 - x = 4 x to be approximately x 0 . 4190597842 . Write the exact solution to this equation. ( Your answer must include logarithms .) (8 points)

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Form A Page 6 of 7 6. Multiple choice. Circle your answer. (3 points each) (a) The Domain of the function f ( x ) = x x - 3 is i. (3 , ) ii. (0 , ) iii. ( -∞ , 3) (3 , ) iv. ( -∞ , 0) (0 , ) (b) Which of the following is equivalent to the expression 2 ln x - ln( x - 3)? i. ln( x 2 ) ln ( x - 3) ii. ln( x ) + ln(3) iii. ln x 2 x - 3 iv. ln( x + 3) (c) Which interval represents the Range of the function whose graph is given be- low? y x i. [ - 1 , 2] ii. [ - 2 , 1] iii. [ - 1 , 1] iv. [0 , 2] (d) The reported cases of the mumps in the United States has been steadily declin- ing. As illustrated in the below table, the number of cases has been reduced by half every 10 years.
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