Question

The number of acres in a region cleared for farming follows the formula a = f (t) = 2t2 where t is the number of months since the region started to be farmed and t ranges from t = 0 to t = 10. Find the average rate of change in the number of acres cleared for farming between t = 1 and t = 4. Give units with your answer

Answer 1

we are given

$a=f(t)=2t^2$

we can use average rate of change formula from t=a to t=b

$A=\frac{f(b)-f(a)}{b-a}$

Here, we are given from t=1 to t=4

so, we will get formula as

$A=\frac{f(4)-f(1)}{4-1}$

now, we can plug values

$A=\frac{2(4)^2-2(1)^2}{4-1}$

now, we can simplify it

$A=10$

the average rate of change in the number of acres cleared for farming between t = 1 and t = 4  is 10 acres/ month.............Answer