Question

Which of these functions could have the graph shown below?

Answer 1

C

`f(x) = 20e ^(x)`

Answer 2

Answer: C) f(x) =
`\tex f(x) =20e^x\tex`

Step-by-step explanation: It is possible to see in the graph that the point (0,20) belongs to the function.

Let's test all the alternatives to see which one works.

We know that x = 0 and y = 20. We should remember that
`x^0 = 1`, ∀x.

A)
`f(x)=20^x \\f(0) = 20^0=1 \\eq 20`

B)
`f(x) = 20^(20x)\\f(0) = 20^(20.0) = 20^0 = 1 \\eq 20`

C)
`f(x) = 20e^(x)\\f(0) = 20e^(0) = 20.1 = 20` ok

D)
`f(x) = e^(20x)\\f(0) = e^(20.0) = e^(0) = 1 \\eq 20`