MATH 1030-008: EXAM 2 REVIEW Origially, I was havig you all memorize the basic compoud iterest formula. I ow wat you to memorize the geeral compoud iterest formula. This formula, whe = 1, is the same as the basic compoud iterest formula. Because they will ot put it o your fial, I wat you to memorize it ow. I would also like you to kow the formulas for the geeral equatio for a lie, the chage i depedet variable, ad the rate of chage. These are all as follows. Memorize the followig: Compoud iterest formula for iterest paid times a year: ( A = P 1 + AP R ) Y Geeral Equatio for a lie: y = mx + b, or depedet variable = rate of chage idepedet variable + iitial value (or y-itercept). Chage i depedet variable: chage i depedet variable = rate of chage chage i idepedet variable Rate of chage: rate of chage = slope = m = chage i depedet variable chage i idepedet variable = rise chage i y ru = chage i x Kow whe ad be able to use the followig: (you do t eed to memorize these) Compoud iterest formula for cotiuous compoudig: Savigs pla formula: Loa paymet formula: A = P MT P MT = [ (AP R Y ) A = P e [ (1 ) ] + AP R (Y ) 1 AP R P AP R ) ] ( Y ) 1 ( 1 + AP R Doublig Time ad Halvig Time formulas: ew value = iitial value 2 t/t double T double 70 P ew value = iitial value ( ) 1 t/thalf 2 T half 70 P Logistic growth: ( ) populatio logistic growth rate = r 1 carryig capacity Equatios for Expoetial fuctios Q = Q 0 (1 + r) t Q = Q 0 2 t/t double Q = Q 0 ( 1 2 ) t/tdouble
1. Suppose you put a sigle deposit of $6, 500 ito a accout with a APR of 5%, compouded daily. How much moey will this be i 7 years? 2. Fid the savigs pla balace after 18 moths with a APR of 6% ad mothly paymets of $300. 3. You put $200 per moth i a ivestmet pla that pays a APR of 4.5%. How much moey will you have after 18 years? Compare this amout to the total deposits made over the time period. 4. You ited to create a college fud for your baby. If you ca get a APR of 7.5% ad wat the fud to have a value of $150, 000 after 18 years, how much should you deposit mothly? 5. Suppose you are 30 years old ad would like to retire at age 60. Furthermore, you would like to have a retiremet fud from which you ca draw a icome of $100, 000 per year forever! How ca you do it? Assume a costat APR of 6%. 6. Assume you have a balace of $5, 000 o your credit card. The credit card APR is 21% ad you wat to pay off the balace i 3 years. Calculate the mothly paymet ad total paymet uder these coditios. Assume you make o additioal charges o your card. 7. You have a car loa of $7, 500 at a fixed APR of 5.8% for 3 years. Calculate your mothly paymets ad also calculate the total amout that you paid i iterest over 3 years.
8. A accout has a APR of 5.3%. You deposit $5, 000. What is your APY whe compoudig occurs quarterly? mothly? daily? 9. Determie whether the followig examples are expoetial or liear growth (or decay). (a) The populatio of Tucso is icreasig at a rate of 3% per year. (b) The price of a gallo of gasolie is icreasig by $0.04 per week. (c) The value of your car is decreasig at a rate of 12% per year. 10. Oil cosumptio is icreasig at a rate of 2.1% per year. What is its doublig time? By what factor will oil cosumptio icrease i te years? 11. Suppose there are 3 bacteria i a bottle at 5 pm ad that the doublig time for bacteria is 3 miutes. How may bacteria will there be i the bottle at 5:09 pm? 12. The half-life of a drug i the bloodstream is 4 hours. By what factor does the cocetratio decrease i 24 hours? 13. Poachig is causig a populatio of elephats to declie by 9% per year. What is the half-life for the populatio? If there are 10,000 elephats today, how may will remai i 50 years?
14. Use the curret aual growth rate of the Uited States, which is about 0.7%, to fid the approximate doublig time of world populatio ad to predict world populatio i 2050 based o a 2000 populatio of 6.0 billio. 15. Oe morig, there were 5 iches of sow o the groud. The the witer storm started ad sow started accumulatig at a costat rate of 3 iches every 2 hours. (a) Idetify the idepedet ad depedet variables: idepedet variable depedet variable (b) Write a liear equatio that describes this situatio. (c) How log did it take for the height of the sow to reach 17 iches? 16. For each of the followig fuctios, fid the slope of the graph ad the y-itercept. The sketch the graph for values of x betwee -10 ad 10. (a) y = 3x + 3 (b) y = 4x + 1 (c) y = 5 (d) y = 2x 17. Suppose your pet dog weighed 2.5 pouds at birth ad weighed 15 pouds after oe year. Based o these two data poits, fid a liear fuctio to predict your dog s weight at 5 ad 10 years of age. Commet o the validity of the model.
18. I 1993, Americas recycled 43.8 millio tos of solid waste. I 1997, the figure grew to about 60.8 millio tos. Fid a liear fuctio that fits the data. Use this fuctio to predict the amout recycled i 2010. (Hit: Assume 1993 is time t = 0. 19. The half-life of aspiri i your blood stream is 3.1 hours. What percet does it decrease by per hour (i.e., what is the rate of decay)? 20. Usig the iformatio i exercise 18, aswer the followig questio. If you take 2 aspiri (650 mg total) at 8 o clock i the morig, at what time should you take a secod dose? (Assume that you take the secod dose whe your headache returs - whe there is oly 100 mg left i your bloodstream.)