Question

Suppose that x and y vary inversely and that y = 83 when x = 8. Write a function that models the inverse variation and find y when x = 4.

Answer 1

y = 664/x

y = 166 when x =4.

Explanation:

Suppose that x and y vary inversely

y ∝ 1/x

y = k/x eq(1)

where k is constant.

Since we have given that

y = 83 when x = 8

Using above values we have to find the value of constant.

83 =k/8

Multiplying above equation by 8,we get

83(8) = (k/8)8

664 = k

Putting the value of constant in eq(1),we get

y = 664/x is equation that models the inverse variation.

We have to find y when x = 4.

y = 664/4

y = 166 when x =4.

Answer 2

1) The function that models the inverse variation is: y=664/x

2) When x=4, y = 166

Explanation:

If x and y vary inversely, then:

y=k/x

where k is a constant. We know that y=83 when x=8, then, replacing in the equation above:

83=k/8

Solving for k: Multiplying both sides of the equation by 8:

8(83)=8(k/8)

664=k

k=664

Then, the function that models the inverse variation is:

y=664/x

2) when x=4:

y=664/x

y=664/4

y=166