Question

question 3 (mandatory) (1 point) which function describes exponential decay? a) $f(x)=6(1.01)^x$ b) $f(x)=3.4(40)^{2x}$ c) $f(x)=8(17)^{\frac{x}{4}}$ d) $f(x)=25(0.8)^x$

Explanation:

Step1: Recall exponential - decay formula

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

Answer:

d) $f(x)=25(0.8)^{x}$