Question

question 22 (mandatory) (1 point) which function describes exponential decay? a) $f(x)=25(0.8)^x$ b) $f(x)=3.4(40)^{2x}$ c) $f(x)=6(1.01)^x$ d) $f(x)=8(17)^{\frac{1}{x}}$

Explanation:

Step1: Recall exponential - decay form

The general form of an exponential - function is $f(x)=a\cdot b^{x}$, where $a
eq0$, $b > 0$, and $b
eq1$. For exponential decay, $0 < b<1$.

Step2: Analyze each option

• Option a: In $f(x)=25(0.8)^{x}$, $a = 25$ and $b = 0.8$. Since $0<0.8<1$, this function represents exponential decay.
• Option b: In $f(x)=3.4(40)^{2x}=3.4(1600)^{x}$, $a = 3.4$ and $b = 1600>1$, so it represents exponential growth.
• Option c: In $f(x)=6(1.01)^{x}$, $a = 6$ and $b = 1.01>1$, so it represents exponential growth.
• Option d: In $f(x)=8(17)^{\frac{1}{x}}$, this is not in the standard form of an exponential - growth or decay function $y = a\cdot b^{x}$.

Answer:

A. $f(x)=25(0.8)^{x}$