Which of the following functions represent exponential

Ответ:

xojade

19.01.2022

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 and

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

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

Thus, and

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, and

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, and

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, and

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

Hence, Option D is not the correct answer.

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