Answer:
Option C is correct
[tex]y = 5 \cdot 4^x[/tex]
Step-by-step explanation:
An exponential function is given by:
[tex]y=ab^x[/tex] .....[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;
[tex]20 = ab[/tex] .....[2]
For (2, 80), we have;
[tex]80 = ab^2[/tex] ......[3]
Divide equation [3] by [2] we have;
[tex]4 = b[/tex]
Substitute this in [2] we have;
[tex]20 = 4a[/tex]
Divide both sides by 4 we have;
5 = a
or
a = 5
Substitute the given values we have;
[tex]y = 5 \cdot 4^x[/tex]
therefore, the following exponential functions goes through the points (1, 20) and (2, 80) is, [tex]y = 5 \cdot 4^x[/tex]
