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, \(y = 5 \cdot 4^x\)
