Answer:
[tex]y = \frac{48}{x}[/tex]
Step-by-step explanation:
Inverse variation:
if [tex]y \propto \frac{1}{x}[/tex]
then the equation is in the form of:
[tex]y = \frac{k}{x}[/tex] ....[1]
where, k is the constant of variation.
As per the statement:
When x = 3, y = 16 and when x = 6, y = 8.
Substitute the value of x and y to find k.
Case 1.
When x = 3, y = 16
then;
[tex]16=\frac{k}{3}[/tex]
Multiply by 3 both sides we have;
48 = k
or
k = 48
Case 2.
When x = 6, y = 8
then;
[tex]8=\frac{k}{6}[/tex]
Multiply by 6 both sides we have;
48 = k
or
k = 48
In both cases, we get constant of variation(k) = 48
then the equation we get,
[tex]y = \frac{48}{x}[/tex]
Therefore, the inverse variation equation can be used to model this function is, [tex]y = \frac{48}{x}[/tex]
