1. Sprint PSC offers a monthly cellular phone plan for $39.99, whi...

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1. Sprint PSC offers a monthly cellular phone plan for $39.99, which includes 350 anytime minutes. The plan charges $0.25 per minute for additional minutes. The piecewise function that models the monthly cost for a subscriber who uses X minutes is 39.99 O39.99+0.25(x-350) X > 350 a. Graph in Excel the monthly cost function. b. Compute the monthly cost for a subscriber using 600 minutes. C. How many minutes were used if the monthly cost was $55.74? 2. A startup company manufactures widgets and sells them for $3.50 each. Their setup cost to produce the widgets was $3500 and they have a variable cost of $0.65 per widget. a. State the revenue function. b. State the cost function. C. State the profit function d. How many widgets must be sold to create a profit of $1000. e. How many widgets must be sold to break even? 3. According to the Bureau of Labor Statistics, the North Carolina unemployment rate for 2008 can be approximated by the function given below, where R(t) represents the unemployment rate in percent and t is the month in 2008 (for example, January 2008 = 1 and October 2008 = 10) 0.28t + 4.44 < t < 9 R(t) = 0.8t -0.93 9a. Evaluate the limit as the month approaches September of 2008 and interpret this answer. Use appropriate limit notation. b. Find lim R(t) / 12 4. The off following chart gives data on credit card debt, where m represents the months after start to pay the card without any new charges and B is the amount you owe after making each you payment. Month 1 5 3 9 7 4 15 14 Balance 1018.9 738.33 867.51 517.87 623.68 795.51 205.86 220.46 a. Graph the data and display on the graph the equation of the curve that best fits the data. The equation that you graph should be one of the following: linear, quadratic, exponential, logarithmic, or power. b. Write the equation that you believe best models the data: C. Why did you choose that model? d. Using your function, predict the balance each month for the first 16 months. e. When will the account balance be paid off? 5. Buddy's Cookies sells boxes of gourmet chocolate chunk oatmeal cookies. The demand function for Buddy's Cookies is given by D(p) = -65p + 560 and the corresponding supply function is given by S(p) = 35p +20, where p is the cost of a box of cookies. a. Find the market equilibrium, and explain your values in the context of the problem. b. If boxes of cookies sell for $4.55, will there be shortage or a surplus? Explain. C. State the Revenue function R(p). What is the company's revenue when cookies are sold at $5 per box? d. Buddy's Cookies has a monthly fixed cost of $750 and variable costs of $0.65 per box of cookies. Write the Cost function, C(p). e. Write the Profit function for the company, Pr(p). f. Buddy's Cookies has decided that they want to keep the price of the cookies below $6.50 per box. In that case, what is the breakeven price for a box of cookies and how many boxes are sold at this price? 6. Past experience has shown a manufacturer that the demand of a product is p = -125-0.25q² a. State the Revenue function. b. How many units must be sold to maximize revenue? What is the maximum revenue? 7. ADZ Technologies is a startup company that specializes in developing apps for Android devices. Their very first year, they made a profit of $65,550. a. The CEO has decided to reinvest the entire profit in a high yield CD. If the company invests the profit for 5 years at a rate of 4.25% compounded quarterly, how much money will the CD be worth after 5 years? b. Another option available to the company is to invest the money at a rate of 3.85% compounded continuously. In this case how long would the company need to keep the money invested to double their initial investment? 8. A business found the price of a fresh whole chicken to be as follows: Weight in pounds of a 5 6 7 8 9 10 11 12 13 14 Whole Chicken Price per pound 1.20 1.15 1.05 1.00 0.95 0.90 0.86 0.80 0.75 0.69 a. Fit a linear trendline to the data, and identify this equation as a reasonable demand function. b. State the revenue function that corresponds to this situation. Assume the above business is willing to supply 25 pounds to a local restaurant at a price of $1.60 per pound and 20 pounds at a price of $1.45 per pound. C. Find the supply function. Assume this is a linear function. d. Using the supply and demand functions identified above, find the point of equilibrium. e. At a price of $1.50, will there be a shortage of chicken or will there be a surplus of chicken? Why? To produce the chickens, the business determines their variable costs to be $0.30 per pound and the fixed costs are $2.50. f. Find the cost function. g. Find the profit function. 9. Evaluate the following limits algebraically. Show the symbolic work. a. lim x->1 x² 2 - 4 b. lim x²+6x+5 x->-1 x2 - 3x - 4 x² 6x 5 C. lim x2 + + x->4 - 3x - 4 10. Use the graph of f(x) to find the limits in parts a - C. A y I 5 a. lim f(x) 4 x->-2 3 2 1 b. lim f (x) x-1 4 . -5 -4 3 -2 1 2 3 4 5 I I O -2 I c. lim f (x) 1 -3 I I I -4 -5 I www.mathwarehouse.com 11. Given f (x)=-3x2+4x-2 find: a. The derivative of f (x) using the definition of derivative. Show all steps. b. The equation of the tangent line for f(x) at x= 2; x=0;x=- - 1 LUS negression A ball is tossed up into the air. Its height as a function of time is given by these data points: t, sec 0.2 0.5 0.8 1.0 1.2 2.0 3.0 height, ft 100 105.8 111.98 116.0 116.01 115.4 99.98 52.2 Use Excel to find the best function to fit the data set and use it to answer the following questions. a) Write the function of best fit using 3 decimals in your coefficients. Also list your R^2 value. b) Predict the height of the ball after 2.5 seconds in flight. c) When does the ball reach 113 feet in the air? d) Find the maximum height of the ball and the time it takes to reach that maximum. CQ4 Limits 6 5 4 a 3 2 1 1 I il 5 - - 3 -2 - I 1 2 3 4 5 6 1 -2 -3 -4 - -5 1. lim f (x) = x-1- 2. lim f(x) = x-(-2) 3. f(-4) = 4. lim f(x) = X-t+00 5. lim f(x) = x-(-4) 6. lim f(x) = x-44+ Evaluate the limit symbolically. Show any work! 2 x-2 x-2 - x b) lim x-Ox-5 x+2 c) lim x->3 x-3 2x+1 d) lim x->00 X-4

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