Question

What is the average rate of change of the functionf(x)=20(14)x from x = 1 to x = 2?

Answer 1

Answer-Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:

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

b−a

f(b)−f(a)

Given the function:

f(x) = 20 \cdot(\frac{1}{4})^xf(x)=20⋅(

4

1

)

x

We have to find the average rate of change from x = 1 to x= 2

At x = 1

then;

f(x) = 20 \cdot(\frac{1}{4})^1 = 5f(x)=20⋅(

4

1

)

1

=5

At x = 2

then;

f(x) = 20 \cdot(\frac{1}{4})^2=20 \cdot \frac{1}{16} = 1.25f(x)=20⋅(

4

1

)

2

=20⋅

16

1

=1.25

Substitute these in above formula we have;

A(x) = \frac{f(2)-f(1)}{2-1}A(x)=

2−1

f(2)−f(1)

⇒A(x) = \frac{1.25-5}{1}=-3.75A(x)=

1

1.25−5

=−3.75

therefore, average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75

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