6.2 Formulas and Modeling 311 29. A P r n 1 ; nt = ⎛ + ⎝⎜ ⎞ ⎠⎟ determine A when P r 1200, 0.04, = = n 2, = and t 5 = (banking). 1462.79 30. A P r n 1 ; nt = ⎛ + ⎝⎜ ⎞ ⎠⎟ determine A when P 100, = r 0.06 = n 1, = and t 3 = (banking). 119.10 In Exercises 31–36, solve the equation for y. 31. x y 6 3 9 + = = − + y x2 3 32. x y 4 2 10 − = = − y x2 5 33. x y6 12 − = = − y x 1 6 2 34. x y 3 10 20 + = = − + y x 3 10 2 35. x y 2 3 6 0 − + = = + y x 2 3 2 36. x y 10 3 0 − = = y x 10 3 In Exercises 37–52, solve for the variable indicated. 37. V IR = for I = I V R 38. i prt r for = = r i pt 39. p a b c a for = + + = − − a p b c 40. v e f 2 − + = for v = − + v e f 2 41. C r r 2 for π = π = r C 2 42. V r h h for 2 π = π = h V r2 43. A bh 1 2 = for b = b A h 2 44. V r h h 1 3 for 2 π = 45. y a bx = + for x = − x y a b 46. y mx b x for = + = − x y b m 47. P l w w 2 2 for = + = − w P l2 2 48. P l w 2 2 = + for l = − l P w2 2 49. = + F C C 32 for 9 5 = − C F 5 9 ( 32) 50. = − C F F ( 32) for 5 9 = + F C 9 5 32 51. A P rt (1 ) = + for r = − r A P Pt 52. A P rt (1 ) = + for t = − t A P Pr Problem Solving In Exercises 53– 60, When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 53. Certificate of Deposit Diya invests $1200 in a certificate of deposit (CD) that pays 5.1% (or 0.051) simple interest for 3 years. a) Use the simple interest formula, i prt, = to determine the amount of simple interest that Diya earns on the CD. $183.60 b) Determine the total value of the CD, including the interest earned, at the end of the 3 years. $1383.60 $ $ π = h V r 3 2 $ 59. Barrel Volume A barrel used to store wax at a car wash is in the shape of a cylinder. The barrel has a radius of 12 inches and a height of 34.5 inches. Determine the volume of the barrel. Use π = V r h. 2 15,607.43 cubic inches a) Use the simple interest formula, i prt, = to determine the amount of simple interest that Parker is charged for the loan. $875 b) Determine the total amount that Parker must pay back at the end of the 5 years. $5875 55. Interest on a Loan Jeff borrowed $800 from his brother for 2 years. At the end of 2 years, Jeff repaid the $800 plus $128 in interest. What simple interest rate did Jeff pay? 8% 56. Simple Interest Earned Jaxon placed $3000 into an investment. After 5 years, Jaxon was repaid the original $3000 plus $1500 in simple interest. Determine the simple interest rate earned on this investment. 10% 57. Driving Time The Burlage family is planning to drive 403 miles from their home in Richmond, Virginia, to the Great Smoky Mountains National Park. If they drive at an average rate of 62 miles per hour, how long will their trip take? Use the formula d rt. = 6.5 hr 58. Travel Rate Uriah traveled from his home in Omaha, NE to visit his cousins in Davenport, IA. The distance traveled was 318 miles and the trip took 4.8 hours to complete. Determine Uriah’s average rate for the trip. Use d rt. = 66.25mph $ $ 54. Simple Interest Loan Parker obtains a small business loan of $5000 to help start a house-painting business. The simple interest rate of the loan is 3.5% (or 0.035) for 5 years. $ m Omaha, Nebraska Michaeljung/Shutterstock AdStock RF/Shutterstock
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