Question

question 14 (mandatory) (1 point) which function describes exponential decay? a) f(x)=25(0.8)^x b) f(x)=8(17)^(x/4) c) f(x)=3.4(40)^(2x) d) f(x)=6(1.01)^x

Explanation:

Step1: Recall exponential - decay formula

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

Step2: Analyze each option

• Option a: $f(x)=25(0.8)^{x}$, here $a = 25$ and $b = 0.8$. Since $0<0.8<1$, this function represents exponential decay.
• Option b: $f(x)=8(17)^{\frac{x}{4}}$, here $b = 17>1$, so it represents exponential growth.
• Option c: $f(x)=3.4(40)^{2x}$, here $b = 40>1$, so it represents exponential growth.
• Option d: $f(x)=6(1.01)^{x}$, here $b = 1.01>1$, so it represents exponential growth.

Answer:

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