A Typical Proportionality Problem:
Finding the Constant of Proportionality

Question:Write an equation for

‘$A\,$ is proportional to the square of $\,t\,,$ and
inversely proportional to the cube of $\,x\,.$’

If $\,A = 3\,$ when $\,t = 1\,$ and $\,x = 2\,,$
find the constant of proportionality.

What is the value of $\,A\,$
when $\, t = -1\,$ and
$\,x = 4\,$?

Solution:

$\displaystyle A = k\cdot \frac{t^2}{x^3}$

Write the equation that describes
the relationship between the variables,
using the information from
Direct and Inverse Variation.
Don't forget the constant of proportionality!