Question

Rewrite the function f(x)=0.25(0.5)⁻³ˣ in the form f(x)=a⋅bˣ. Write a and b as whole numbers, decimals, or simplified proper or improper fractions.

f(x)=21​(2)⁻³ˣ
f(x)=41​(2)⁻³ˣ
f(x)=21​(0.5)⁻³ˣ
f(x)=41​(0.5)⁻³ˣ

Now use the function in its new form to complete the sentence. When x increases by 1, the function ______ by a factor of ______.

A. increases; 2
B. decreases; 2
C. increases; 0.5
D. decreases; 0.5

Answer 1

The function is rewritten as f(x) = 1/4 (2)³ˣ

When x increases by 1, the function f(x) increases by a factor of 2

How to write the function

The function f(x) = 0.25 (0.5)⁻³ˣ can be rewritten in the form f(x) = a ⋅ bˣ as follows:

a = 0.25 = 1/4

b = 0.5⁺¹ = 2

f(x) = 1/4 (2)³ˣ

The function in the desired form is f(x) = 1/4 (2)³ˣ

Now, to complete the sentence, when x increases by 1, the function f(x) increases by a factor of 2. Therefore, the correct answer is:

A. increases; 2