Question

Find the Rate of Change of the function h(x)=2^x on the interval 2 ≤ x ≤ 4.

Answer 1

The rate of change is 6.

Explanation:

Answer 2

Rate of change of function
`h(x) = 2^x` on the interval
`2\leq x\leq 4` is; 6.

Explanation:

Given the function:
`h(x) = 2^x` on the interval
`2\leq x\leq 4`

Rate of change of function: Let f be the function defined on the interval
`a\leq x\leq b`, then the rate of change of function A(x) is given by:

A(x) =
`(f(b)-f(a))/(b-a)`

at x = 2;

h(2) =
`2^2= 4`

and at x = 4

h(4) =
`2^4= 16`

then, by the definition of rate of change of function:

A(x) =
`(h(4)-h(2))/(4-2)`

Substitute the value of h(2) = 4 and h(4) = 16 we have;

`A(x) = (16-4)/(4-2)=(12)/(2) = 6`

Therefore, the rate of change of function is 6.