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#### Expansion and factorisation.

#### Modelling with functions.

**LIQUID LOSS INVESTIGATION**

**YEAR 10A ASSIGNMENT**

*Technology Active – the use of calculator is advised for this assignment.*

A new dry-cleaning machine has been designed. At the end of each cleaning cycle, the dry-cleaning liquid will be reduced by evaporation and condensation. Each time the machine is used there is a loss of 2% of the dry-cleaning liquid.

Initially the machine is filled with 1000 mL of dry-cleaning liquid.

- How much liquid will remain after the machine has been used once, twice and five times? Give your answers correct to the nearest mL.
- Develop a formula that uses indices to determine the amount of liquid
*A*(in mL) left after*n*uses. - Use your formula to check your answers from question 1.
- Sketch the graph of
*A*versus*n*for . Use appropriate scale on each axis. - Determine which is dependent and which is independent variable.
- What name do we give to the graph of
*A*versus*n*? - Show that after 20 uses the quantity of liquid remaining is approximately two-thirds of the original quantity.
- How much liquid will remain after 40 uses? What proportion is this of the original quantity?
- If the original quantity of liquid was 2000 mL, change your formula appropriately and redo the calculations for question 8.
- Make a comparison of your answers to questions 8 and 9. What do you notice?
- When the quantity of liquid is reduced to of the original amount it is time to replace the liquid. After how many uses will the liquid need to be replaced?
- What amount of liquid would initially be required if the amount remaining when the liquid needs replacing is 200 ml?