Question

question 6 (mandatory) (1 point) which function describes exponential decay? a) f(x)=8(1.7)^x b) f(x)=3.4(4.0)^x c) f(x)=2.5(0.8)^x d) f(x)=6(1.01)^x

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - function is $y = a(b)^x$, where $a>0$. For exponential decay, $0 < b<1$.

Step2: Analyze each option

• Option a: $f(x)=8(17)^x$, here $b = 17>1$, so it is exponential growth.
• Option b: $f(x)=34(40)^x$, here $b = 40>1$, so it is exponential growth.
• Option c: $f(x)=25(0.8)^x$, here $a = 25>0$ and $b=0.8$ with $0 < 0.8<1$, so it is exponential decay.
• Option d: $f(x)=6(1.01)^x$, here $b = 1.01>1$, so it is exponential growth.

Answer:

C. $f(x)=25(0.8)^x$