Construct Inverse Proportion Equations

## Construct Inverse Proportion Equations

If the relationship is an inverse proportion, then write the proportionality equation as:

y prop frac(1)(x)

Then change prop to = and multiply one side of the equation by k:

y prop frac(k)(x)

Remember that the x or the y might be a value such as x^2 or sgrt(x) or other power term.

## Example 1

An experiment showed that the number of bacteria in a dish was inversely proportional to the square of the temperature.

One dish at 24℃ had 18,000 bacteria. How many bacteria would you expect there to be in a dish at 20℃?

 Proportion is n prop frac(1)(t^2) Create equation with k n = frac(k)(t^2) Substitute 18000 = frac(k)(24^2) Solve k = 10368000 n = frac(10368000)(t^2) When temp = 20 n = frac(10368000)(20^2) n = 25920

An experiment showed that a temperature, t, was inversely proportional to the square root of a height, h. When the height was 400m, the temperature was 20℃.
 Proportion is t prop frac(1)(sqrt(h)) Create equation with k t = frac(k)(sqrt(h)) Substitute 20 = frac(k)(sqrt(400)) Solve k = 400 t = frac(400)(sqrt(h)) When height = 1000 t = frac(400)(sqrt(1000)) t = 12.649 t = 12.6 (1dp)