The temperature, 7, in C, of a potato put into an oven is given as a function of time, t, in minutes, by 7 = a(1 - e-kt) + b. (a) Knowing that the temperature of the potato is initially 17C tells us that O T(0) = 17 O T'(0) = 17 O T(17) = 0 O T ' (17 ) = 0 Knowing that the temperature of the oven is a constant 275C tells us that O lim T(t) = 17 t -0 O lim T(t) = 00 t - 00 O lim T(t) = 275 t - 00 O lim T(t) = 275 t - 0 (b) Use the information in part (a) to find the exact values of a and b. a = b = (c) Knowing that the temperature of the potato is initially increasing 3C per minute tells us that OT'(0) = 3 O T ' ( 3 ) = 0 O T(1) = 20 O T(0) = 3 O T(3) = 0