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An exponential function is given by the equation [tex]f(x)=10 \cdot\left(\frac{1}{18}\right)^x[/tex]. Does the function represent growth or decay?

A. The function represents exponential decay because the base equals [tex]\frac{1}{18}[/tex].
B. The function represents exponential growth because the base equals [tex]\frac{1}{18}[/tex].
C. The function represents exponential growth because the base equals 18.
D. The function represents exponential decay because the base equals 18.

Sagot :

GinnyAnsweridn
To determine whether the exponential function [tex]\( f(x) = 10 \cdot \left(\frac{1}{18}\right)^x \)[/tex] represents exponential growth or decay, we need to examine the base of the exponential component.

1. The given function is [tex]\( f(x) = 10 \cdot \left(\frac{1}{18}\right)^x \)[/tex].

2. The base of the exponential term is [tex]\(\frac{1}{18}\)[/tex].

3. In the context of exponential functions, if the base of the exponent is greater than 1, the function represents exponential growth. Conversely, if the base is between 0 and 1, the function represents exponential decay.

4. Here, the base [tex]\(\frac{1}{18}\)[/tex] is a fraction between 0 and 1, as [tex]\(\frac{1}{18} < 1\)[/tex].

5. Since the base is less than 1, we can conclude that the function represents exponential decay.

Therefore, the function represents exponential decay because the base equals [tex]\(\frac{1}{18}\)[/tex].
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