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.

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` |

Answer:

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℃.

What was the temperature at 1000m? give your answer to 1 decimal place.

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)` |

Answer: 12.6℃

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