As the variables vary inversely, we have the following relationship:
[tex]y = k / x
[/tex]
From here, we must find the value of the constant k.
For this, we use the following data:
x = 10 when y = 8
Substituting values we have:
[tex]8 = k / 10
[/tex]
From here, we clear the value of k:
[tex]k = (8) * (10)
k = 80[/tex]
Substituting the value of k we have that the function is:
[tex]y = 80 / x
[/tex]
Then, for x = 5 we have:
[tex]y = 80/5
y = 16[/tex]
Answer:
The function that models the inverse variation is:
[tex]y = 80 / x
[/tex]
when x = 5:
[tex]y = 16[/tex]
