Question

Which of the following functions represent exponential decay?

Answer 1

Option C: $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$ is the function that represent exponential decay.

Explanation:

The exponential decay can be represented by

$f(x)=a \cdot b^{x}$ where $a>0$ and $0$

Option A: $f(x)=3(1.7)^{x-2}$

From the function, we can see that $a=3$ and $b=1.7$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3(1.7)^{x-2}$ does not represent exponential decay.

Hence, Option A is not the correct answer.

Option B: $f(x)=3(1.7)^{-2 x}$

From the function, we can see that $a=3$ and $b=1.7$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3(1.7)^{-2 x}$ does not represent exponential decay.

Hence, Option B is not the correct answer.

Option C: $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$

From the function, we can see that $a=3^5=243$ and $b=\frac{1}{3} =0.3333$

Thus, $a>0$ and $0$

Thus, the function $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$ represent exponential decay.

Hence, Option C is the correct answer.

Option D: $f(x)=3^{5}(2)^{-x}$

From the function, we can see that $a=3^5=243$ and $b=2$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3^{5}(2)^{-x}$ does not represent exponential decay.

Hence, Option D is not the correct answer.