64-65 Find equations of the tangent line and normal line to the curve at the given point. 64. x2 + 4):}! + y2 =13, (2,1) 65. y = (2 + x)e_"', (0, 2) 97. A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the popula- tion has increased to 360 cells. (a) Find the number of cells after t hours. (b) Find the number of cells after 4 hours. (c) Find the rate of growth after 4 hours. ((1) When will the population reach 10,000? 98. Cobalt-6O has a halflife of 5.24 years. (a) Find the mass that remains from a 100-mg sample after 20 years. (b) How long would it take for the mass to decay to 1 mg? 100. A cup of hot chocolate has temperature 80C in a room kept at 20C. After half an hour the hot chocolate cools to 60C. (a) What is the temperature of the chocolate after another half hour? (b) When will the chocolate have cooled to 40C? 106. (3) Find the linear approximation to f(x) = 25 x2 near 3. (b) Illustrate part (a) by graphing f and the linear approximation. 107. (a) Find the linearization of f(x) = 3/1 + 3x at a = 0. State the corresponding linear approximation and use it to give an approximate value for 3/ 1.03