The number N of bacteria in a refrigerated food is given by

Question

N(T) = 10T2 − 20T + 700, 1 ¡Ü T ¡Ü 20where 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, 0 ¡Ü t ¡Ü 6 where t is the time in hours.
(a) Find the composition N(T(t)).
N(T(t)) = 1
, 0 ¡Ü t ¡Ü 6

Answer 1

N(t) = 10t^2 - 20t + 700
N(T(t)) = 10T^2 - 20T + 700
= 10(5t+2)^2 - 20(5t+2) + 700
= 250t^2 + 100t + 700