Question

Suppose that w and t vary inversely and that t= 1/5 when w = 4. Write a function that models that inverse variation, and find t when w = 9

Answer 1

Step 1:

Write an equation that shows that w and t vary inversely

`\text{w = }(k)/(t)`

Step 2:

`\begin{gathered} Use\text{ w = 4 and t = }(1)/(5)\text{ to find k} \\ 4\text{ = }(k)/((1)/(5)) \\ \text{4 = 5k} \\ \text{k = }(4)/(5) \end{gathered}`

Step 3

`\begin{gathered} w\text{ = }(4)/(5t) \\ 9\text{ = }(4)/(5t) \\ 5t\text{ }*\text{ 9 = 4} \\ 45t\text{ = 4} \\ \text{t = }(4)/(45) \end{gathered}`

Final answer

`\begin{gathered} Function\text{ that models that inverse variation is w = }(4)/(5t) \\ t\text{ = }(4)/(45) \end{gathered}`