Question

In exercises 13 and 14, determine a formula for the exponential function.

a) f(x)=eˣ
b) f(x)=2ˣ
c) f(x)=x
d) f(x)=ln(x)
e) f(x)=10ˣ

Answer 1

The exponential functions among the given options are
`\( f(x) = e^x \)`,
`\( f(x) = 2^x \)`, and
`\( f(x) = 10^x \)`, A, B and E.

How to determine formula?

The task is to determine a formula for an exponential function. An exponential function typically has the form
`\( f(x) = a^x \)`, where a is a positive constant (the base of the exponential function), and x is the variable.

To go through each option:

a)
`\( f(x) = e^x \)`

This is already in the form of an exponential function. Here, a = e (where e is Euler's number, approximately equal to 2.71828).

b)
`\( f(x) = 2^x \)`

This is also an exponential function with a base of 2.

c)
`\( f(x) = x \)`

This is not an exponential function. It's a linear function.

d)
`\( f(x) = \ln(x) \)`

This is not an exponential function. It's the natural logarithm function, which is the inverse of the exponential function
`\( e^x \)`.

e)
`\( f(x) = 10^x \)`

This is an exponential function with a base of 10.

In summary:

The exponential functions among the given options are
`\( f(x) = e^x \)`,
`\( f(x) = 2^x \)`, and
`\( f(x) = 10^x \)`.

The other functions,
`\( f(x) = x \)` and
`\( f(x) = \ln(x) \)`, are not exponential functions.

Complete question:

In exercises 13 and 14, determine a formula for the exponential function f(x)=aˣ.

a) f(x)=eˣ

b) f(x)=2ˣ

c) f(x)=x

d) f(x)=ln(x)

e) f(x)=10ˣ