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Test1_Ma131 - y n c Use the solution to find y 99 5(13 pts...

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Test #1 – Make-up Math 131 Calculators allowed. Be sure to show all your work. 1. (15 pts) Given the function, f ( x ) = x a. Find the tangent line to the graph at x = 4, write it in slope-intercept form. b. Use the tangent line to approximate 4.1 . c. What would be the slope of a line perpendicular to the tangent line. 2. (14 pts) Suppose you deposit 5,000 dollars in a savings account, on which the bank pays 6 percent interest compounded monthly. Just before the end of each month, you make an additional deposit of 150 dollars. a. Write down an equation that can be used to calculate the balance of the account at the end of the month in terms of the balance at the start of the month. y n +1 = ay n + b b. Solve the different equation and use this to find the amount in the account after 20 years. 3. (12 pts) Find the derivative of ONE of the following functions using the three step method. f ( x ) = 3 x 2 + 4 x +1 f ( x ) = 5 x - 2 4. (15 pts) Given y n +1 = 2 y n + 3 y 0 =1 a. Find the first two terms. b. Solve the equation for the explicit solution for
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Unformatted text preview: y n c. Use the solution to find y 99 5. (13 pts) Draw a rough sketch of the difference equation without generating terms or solving the equation. (Be sure to show the asymptote, a sketch of a few points, label either mono or osc, label either repel or attract) y n +1 = 3 y n +10 y =10 6. (16 pts) Derek has just retired, and has 700,000 dollars in his retirement account. The account will earn interest at an annual rate of 6 percent, compounded monthly. At the end of each month, Derek will withdraw a fixed amount to cover his living expenses. a. Derek wants his savings to last exactly 20 years. How much money can he withdraw each month? b. What is the maximum amount that Derek can withdraw each month if he wants his savings to last indefinitely? 7. (15 pts) Find the derivative of the following functions. f ( x ) = x 9 g ( x ) = 1 x 3 h ( x ) = 9...
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