a function is given. f(t) = 6t^2 + t; t = 3, t = 5 (a) determine the net change between the given values of…

Explanation:

Step1: Calculate f(5)

Substitute (t = 5) into (f(t)=6t^{2}+t). [ \begin{align*} f(5)&=6\times5^{2}+5\ &=6\times25 + 5\ &=150+5\ &=155 \end{align*} ]

Step2: Calculate f(3)

Substitute (t = 3) into (f(t)=6t^{2}+t). [ \begin{align*} f(3)&=6\times3^{2}+3\ &=6\times9+3\ &=54 + 3\ &=57 \end{align*} ]

Step3: Find net - change

The net - change of the function (y = f(t)) from (t=a) to (t = b) is (f(b)-f(a)). Here (a = 3), (b = 5), so the net - change is (f(5)-f(3)=155 - 57=98).

Step4: Find average rate of change

The average rate of change of the function (y = f(t)) from (t=a) to (t = b) is (\frac{f(b)-f(a)}{b - a}). Here (a = 3), (b = 5), and (f(5)-f(3)=98), (b - a=5 - 3 = 2). So the average rate of change is (\frac{98}{2}=49).

Answer:

(a) 98 (b) 49