Question

The graphs of the functions f(x) = 46° ¹* 40 -8 Home –20 -2 A. green B. blue C. red are shown below. If the graph of f(x) = 46° is blue, then the graph of f(x) = 4 v - D. not shown 054 (1) and 8 10 12 14 16 18 20 0.5 is​

Answer 1

A. green

Explanation:

The equation of a basic exponential function is given as f(x) = a(r)ˣ.

For all of the given functions, a=4. You need to determine what r is in each case, to determine which graph matches the requested function (if shown).

`f(x)=4e^(0.1x)`:
`e^(0.1x)=(e^(0.1))^x` and
`e^(0.1)=r` ≈1.1052

`f(x)=4(1+(0.1)/(0.5))^(0.5x)`:
`(1+(0.1)/(0.5))^(0.5x)=[(1+(0.1)/(0.5))^(0.5)]^x` and
`(1+(0.1)/(0.5))^(0.5)=r`≈1.0954

`f(x)=4(1+(0.1)/(2))^(2x)`:
`(1+(0.1)/(2))^(2x)=[(1+(0.1)/(2))^(2)]^x` and
`(1+(0.1)/(2))^2=r=1.1025`

Since 1.0954 is the smallest, the graph of
`f(x)=4(1+(0.1)/(0.5))^(0.5x)` will be shallower than the other two graphs, making it the green one.