A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r (in feet) of the outer ripple is given by r(t) = 0.9!; where t is time in seconds after the pebble strikes the water. The area A of the circle is given by the function A(r) = M2. Find and interpret (A o r)(t). (A ., rxt) =| I (A o r)(.':) represents the increase in area from time tto time t + 1. (A o r)(t) represents the distance from the outer ripple to the center of the pond. (A o r)(t) represents the circumference of the outer ripple. (A o r)(.':) represents the area of the circle at time t. The number N of bacteria in a refrigerated food is given by mm = 10T2 20T+ 500, 1 5 T5 20, where T is the temperature of the food in degrees Celsius. When the food is removed from refrigeration, the temperature of the food is given by T(t)=5t+2, 05:56 where t is the time in hours. (a) Find (N a T)(t). (NoT)(t)=| |,Ost56 Interpret (N a D\"). This represents the rate at which the temperature of the food is changing as a function of time. This represents the rate at which the number of bacteria in the food is increasing as a function of time. This represents the increase in the number of bacteria in the food from time t to t + 1. This represents the number of bacteria in the food as a function of time. (b) Find the bacteria count after 0.5 hour. (Round your answer to the nearest whole number.) N(T(O.5)) = bacteria (c) Find the time when the bacteria count reaches 2250. (Round your answer to three decimal places.)