Question

Which of the following exponential functions goes through the points (1, 20) and (2, 80)?

f(x) = 5(4)^−x
f(x) = 4(5)^−x
f(x) = 5(4)^x
f(x) = 4(5)^x

Answer 1

f(x) = 5(4)^x is the correct answer.

Answer 2

Option C is correct

`y = 5 \cdot 4^x`

Explanation:

An exponential function is given by:

`y=ab^x` .....[1]

where, a is the initial value and b is a non-negative number.

As per the statement:

An exponential functions goes through the points (1, 20) and (2, 80)

Substitute these in [1] we have;

For (1, 20) we have;

`20 = ab` .....[2]

For (2, 80), we have;

`80 = ab^2` ......[3]

Divide equation [3] by [2] we have;

`4 = b`

Substitute this in [2] we have;

`20 = 4a`

Divide both sides by 4 we have;

5 = a

or

a = 5

Substitute the given values we have;

`y = 5 \cdot 4^x`

therefore, the following exponential functions goes through the points (1, 20) and (2, 80) is,
`y = 5 \cdot 4^x`