Question

question 20 (mandatory) (1 point) which function describes exponential growth? a) $f(x)= - 24(-6)^{x}$ b) $f(x)=18.9(10)^{\frac{x}{4}}$ c) $f(x)=180(0.95)^{x}$ d) $f(x)=13.7(\frac{1}{5})^{x}$

Explanation:

Step1: Recall exponential - growth formula

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

Step2: Analyze option a

For $f(x)=-24(-6)^{x}$, $a=-24<0$ and the base $-6$ is negative. Exponential functions with negative bases are not well - defined for all real numbers and do not represent exponential growth.

Step3: Analyze option b

For $f(x)=18.9(10)^{\frac{x}{4}}$, here $a = 18.9>0$ and $b = 10>1$. This function represents exponential growth.

Step4: Analyze option c

For $f(x)=180(0.95)^{x}$, since $0 < 0.95<1$, this function represents exponential decay.

Step5: Analyze option d

For $f(x)=13.7(\frac{1}{5})^{x}$, since $0<\frac{1}{5}<1$, this function represents exponential decay.

Answer:

B. $f(x)=18.9(10)^{\frac{x}{4}}$