ame screen. 51. Biologists have proposed a cubic polynomial to model the length L of Alaskan rockfish at age A: Зх — у- E 60. At what L= 0.0155A³ - 0.372A? + 3.95A + 1.21 line par: where Lis measured in inches and A in years. Calculate the cur 61. Find an dL that is dA A=12 62. Where and interpret your answer. the por 52. The number of tree species S in a given area A in the Pasoh Illustra Forest Reserve in Malaysia has been modeled by the power 63. Draw function the pa S(A) = 0.882A0.842 Find where A is measured in square meters. Find S' (100) and interpret your answer. inters 64. (a) Source: Adapted from K. Kochummen et al., "Floristic Composition of Pasoh Forcst Rescrve, A Lowland Rain Forcst in Pcninsular Malaysia," Journal of (b) Tropical Forest Science 3 (1991):1–13. 53. Boyle's Law states that when a sample of gas is compressed 65. Us at a constant temperature, the pressure P of the gas is inversely proportional to the volume V of the gas. (a) Suppose that the pressure of a sample of air that occu- pies 0.106 m at 25°C is 50 kPa. Write V as a function the ca 66. F fi of P. (b) Calculate dV/dP when P = 50 kPa. What is the mean- ing of the derivative? What are its units? 67. I A 54. Car tires need to be inflated properly because overinflation or underinflation can cause premature tread wear. The data 68. in the table show tire life L (in thousands of miles) for a certain type of tire at various pressures P (in lb/in*). 42 38 35 31 28 26 70 74 81 78 66 50 L. 69 (a) Use a calculator to model tire life with a quadratic func- tion of the pressure. al to octimate dL/dP when P = 30 and 459