Question

Which of the following options results in a graph that shows exponential growth?

a. f(x) = 0.4(3)x
b. f(x) = 3(0.5)x
c. f(x) = 0.8(0.9)x
d. f(x) = 0.9(5)−x

Answer 1

F(x)=0.4(3)^x

Explanation:

Answer 2

A function
`f(x)=b\cdot a^x` shows

• exponential growth, if
  `a>1;`
• exponential decay, if
  `0<a<1.`

Consider all options:

A. The function
`f(x)=0.4\cdot 3^x` shows exponential growth, because
`3>1.`

B. The function
`f(x)=3\cdot 0.5^x` shows exponential decay, because
`0<0.5<1.`

C. The function
`f(x)=0.8\cdot 0.9^x` shows exponential decay, because
`0<0.9<1.`

D. The function
`f(x)=0.9\cdot 5^(-x)=0.9\cdot \left((1)/(5)\right)^x` shows exponential decay, because
`0<(1)/(5)<1.`

Answer: correct choice is A