Suppose that an and b vary inversely and that b= 5/4 when a = 8. Write a function that models the inverse variation
The general formula for inverse variation is:
y = k/x
Where k is a constant, and y and x are the two variables that vary inversely. In this case, we have:
b = k/a
We can find the value of k by using the given information:
b = 5/4 when a = 8
5/4 = k/8
k = 10
Therefore, the function that models the inverse variation is:
b = 10/a
To write a function that models inverse variation, we can use the equation:
ab = k
where "a" and "b" are the variables that vary inversely, and "k" is a constant.
Now, to find the value of "k" using the given information, we can substitute the values of "a" and "b" from the problem into the equation:
(8)(5/4) = k
Simplifying, we get:
10 = k
Therefore, the equation that models the inverse variation is:
ab = 10
To write a function that models the inverse variation between the variables a and b, we can use the formula for inverse variation:
a * b = k
Where "k" is the constant of variation. According to the given information, when a = 8, b = 5/4. We can substitute these values into the formula to solve for k:
8 * (5/4) = k
40/4 = k
k = 10
Now that we have determined the value of the constant of variation, the function that models the inverse variation is:
b = k / a
Substituting the value of k we found:
b = 10 / a
Therefore, the function that models the inverse variation is b = 10 / a.