Question

What is the average rate of change for ƒ(x) = −2^x + 70 over the interval 2 ≤ x ≤ 6? A) −15 B) −16 C) −30 D) −32

Answer 1

Answer:

-15

Step-by-step explanation:

15 is the average rate of change for ƒ(x) = −2x + 70 over the interval 2 ≤ x ≤ 6.

ƒ(b) − ƒ(a)

b − a

=  

ƒ(6) − ƒ(2)

6 − 2

=  

6 − 66

4

=  

−60

4

= −15

Answer 2

Answer:

A

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [a, b ] is

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

Here [ a, b ] = [ 2, 6 ], thus

f(b) = f(6) = - $2^{6}$ + 70 = - 64 + 70 = 6

f(a) = f(2) = - 2² + 70 = - 4 + 70 = 66

average rate of change = $\frac{6-66}{6-2}$ = $\frac{-60}{4}$ = - 15 → A