Math 122 Calculus for Business Admin. and Social Sciences
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1 Math 122 Calculus for Business Admin. and Social Sciences nstructor: Ann Clifton Name: SoLs Exam #1 A July 3, 2018 Do not turn this page until told to do so. You will have a total of 1 hour 40 minutes to complete the exam. Unless otherwise stated, you must show all work to receive full credit. Unsupported or otherwise mysterious answers will not receive credit. f you require extra space, use the provided scrap paper and indicate that you have done so. You may use a calculator without a CAS if you like, but a calculator is not necessary. NO PHONES ALLOWED. Draw a firework on this page if you read these directions in full. Cheating of any kind on the exam will not be tolerated and will result in a grade of 0%. # score out of # score out of EFFEEFFE Total 100 Remember: This exam has no impact on your worth as a human being. You got this!!!
2 1. (a) State the Point-Slope form of a line passing through the point (x 0,y 0 ) with slope m. y yo mcx Xo (b) State the Slope-ntercept form of a line with slope m and y-intercept b. y mxtb 2. Let f be a function and let a<bbe given. State the average rate of change of f on the interval [a, b]. f b t's b a f a 3. Given a quantity P 0, state the relative change of the quantity from P 0 to P 1. S P Po Too Neo geo 2
3 4. (a) State the form of an exponential function of a variable t with initial value P 0 and base a: (b) The relative rate of change of P is 1 Poat P (t) =. a r =. [Hint: f you don t recall the formula, this is just the relative change from P (t) top (t + 1).] (c) The function P models (i) exponential growth when r is. (ii) exponential decay when r is. (d) The continuous growth/decay rate is lpositive negative Hlnla k =. 5. Let 0 <x,0<ybe given. Fill in the blanks: (i) ln(1) = (iv) ln(x r )= 0 H rlncx (ii) ln(xy) = lmk tlnly (v) ln(e x )= H X x (iii) ln = y (vi) e ln(x) = lnlx ndy 1 X 3
4 6. (a) Find the slope of the line passing through the points (3, 1 2 ) and (2, 1). m t k (b) Write the equation of this line in Point-Slope Form. 1 2 Y (c) Write the equation of this line in Slope-ntercept Form. 2 y (d) Sketch a graph of f(x). Label the x-intercept and the y-intercept. 2 t it 4
5 7. Let f(x) = x (a) Compute the average rate of change for f between x = 3 and x = 5. 3 f s f (b) Give the Point-Slope form of the line that passes through (3,f(3)) and (5,f(5)). z M 8 bypart a y 18 8 x 3 (c) Give the Slope-ntercept form of the line from part (b). 3 y
6 8. A biologist observes a population with initial size 9. n two years, the biologist returns to observe the population again and finds that there are 81. (a) Find an exponential function for the size of the population as a function of t years since the initial observation. Po 9 pct 9 at of Pct a t (b) Does the function from part (a) model growth or decay? 4 Growth (c) Use the model from part (a) to determine how many years it will take for the size of the population to reach t 27 3 t t 3 years 6
7 S 9. A bank is o ering an account that pays 8% interest compounded continuously. f you decide to invest money in this account, how long will it take for your initial investment to double? Round to the nearest year. Rule of fo 70T 9 years OR 2 le 08t n 2 08 t t years 7
8 S 10. Let f(t) be the number of US billionaires in year t. Express the following statements in terms of f. (a) n 1985 there were 13 US billionaires. 2 f (b) n 1990 there were 99 US billionaires. 2 f (c) Find the average yearly increase in the number of US billionaires between 1985 and Express this using f. S f 1990 f 1985 Fgs ,2 (d) Assuming the yearly increase remains constant, find a formula predicting the number of US billionaires in year t. 6 y t 1985 y t 34,142 y f t _17.2T 34,129 8
9 A company hosts a weekly event. They find that 25 people attend at a ticket price of $30, and 15 people attend at a ticket price of $50. Assuming this relationship is linear, determine the ticket price that will generate the highest revenue. State the maximum revenue. Hint: First, find the equation of the line representing the quantity of tickets sold, q, in terms of price, p. pig 3 73 m o KS q p 30 q Pt S q kept 40 S R p p.q pftzpt40 YzpZt4Op Vertex tha fl bras tat 4 4 S R S 9
Math 122 Calculus for Business Admin. and Social Sciences
Math 122 Calculus for Business Admin. and Social Sciences Instructor: Ann Clifton Name: Exam #1 A July 3, 2018 Do not turn this page until told to do so. You will have a total of 1 hour 40 minutes to complete
Page Points Score Total: 100
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