Question

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

Answer 1

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

Answer 2

Answer:

Option C is correct

$y = 5 \cdot 4^x$

Step-by-step 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, $y = 5 \cdot 4^x$