The number N of bacteria in a refrigerated food is given by
N(T) = 10T2 − 20T + 600, 2 ≤ T ≤ 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) = 3t + 2, 0 ≤ t ≤ 6
where t is the time in hours.
(a) Find and interpret (N ∘ T)(t).
(b) Find the bacteria count after 0.5 hour.
(c) Find the time when the bacteria count reaches 1500.