What is the average rate of change of a function

Asked by admin @ 28/10/2021 in Mathematics viewed by 280 People

What is the average rate of change of the function f(x)=480(0.3)× from x=1 to x=5

Answered by admin @ 28/10/2021

Answer:

The average rate of change(A(x)) of a function f(x) from a to b as;

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

Given the function: $f(x) = 480(0.3)^x$

For x =1 ,

$f(x) = 480(0.3)^1 = 480\cdot 0.3 = 144$

and for x=5

$f(x) =480(0.3)^5 = 480 \cdot 0.00243= 1.1664$

then;

the average rate of change of a function A(x)= $\frac{f(5)-f(1)}{5-1}$ or

$A(x) =\frac{1.1664-144}{4}= \frac{-142.8336}{4}= -35.7084$

Therefore, the average rate of change of the given function from x=1 to x=5 is; -35.7084

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