Science:Math Exam Resources/Courses/MATH102/December 2016/Question A 05/Hint 1

The average rate of change $A={\frac {\Delta T}{\Delta t}}={\frac {T(12)-T(5)}{12-7}}$ is the slope of the secant line through the points $(5,T(5))$ and $(12,T(12))$ , whereas $T'(5)$ and $T'(12)$ represent the slope of the tangent line at the points $(5,T(5))$ and $(12,T(12))$ respectively.

Recall that the (instantaneous) rate of change of the temperature of an object is given by $T'(t)=k(E-T)$ , where $E$ is the ambient temperature and k is a positive constant.