# Rate of change

##### Examples

###### Lessons

- Draw a graph to describe the fare charged by a taxi with an initial cost of $10.50 plus $2.50 per km traveled.
- Draw a graph to describe the income of a insurance sales person who earns $800 per month plus $400 for every car sold.
- A long distance runner passes the 36 km mark of a race in 1 hr 40 mins, and passes the 44 km mark 1 hr 10 mins later. If the rate is constant, find the speed of the long distance runner in km/hr.
- Cathy hires a super band to play at a wedding. The cost for the wedding was $1000 for the band, plus $50 per guest for food and $3 per guest for beverages. Determine the cost per person if 150 guests attended the wedding, and averaged three drinks per person.

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###### Topic Notes

Rate of change is all around us. For example, we express the speed of a car as Kilometer per hour (km/hr), the wage in a fast food restaurant as dollar per hour, and taxi fare as dollar per meter or kilometer. Let's solve some word problems on rate of change.

Rate of change = ${{{\bigtriangleup y} \over {\bigtriangleup x} } = { {y_2 -y_1} \over {x_2 -x_1}}}$Examples: km/hr, miles per gallon, m/s, dollars/hr, etc.

###### Basic Concepts

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