Project #59815 - GENERAL MATHS FOUNDATION - INVESTIGATION THE CANDLE CLOCK

In the medieval times a notched candle was sometimes used as a clock. In this investigation you will discover how the height of a birthday candle is related to the time spent burning.

 

Measure the length of a birthday candle every half minute over a five minute period.

 

(Use this data)


Time (mins)    Length (cm)

 0                         6.3

0.5                       5.0

1.0                       4.5

1.5                       4.0

2.0                       4.0

2.5                       4.0

3.0                       3.8

3.5                       3.5

4.0                       3.3

4.5                       3.3

5.0                       2.8               

 

 

2. Plot a graph of your results. You can cut and paste if you prefer to do the graph on a separate graph paper.

 

 

3. Find the linear equation between the candles length (L) and the time that it has been burning (T) - use the regression function.

 

 

 

 

 

 

 

 

 

4. What is the value of the y-intercept and what does it represent in the context of this investigation?

 

 

 

 

 

 

 

 

 

5. Use algebra and your answer to question 3 to find the value of the x-intercept (if the graph was extended), and what does it represent?

 

 

 

 

 

 

 

 

 

6. What is the gradient and what does it represent in the context of this investigation?

 

 

 

 

 

 

 

 

 

7. Use your equation to find the length of the candle after 3 1/2 minutes.

 

 

 

 

 

 

 

 

 

8. Use your equation to predict the time at which your candles would be 1 cm long.

 

 

 

 

 

 

 

 

 

9. How long a candle (of the same diameter) would you need if you wished it to burn for an hour?

 

 

 

 

 

 

 

 

 

10. A “Birthday Bash” candle is such that its length (in cm) is given by the equation:

 

L = -0.1t + 9

 

An “Intimate Moments” candle is such that its length is given by the equation:

 

L = -0.06t + 7

 

Use the equation to identity and describe differences between the two candles.

 

 

 

 

 

 

 

 

 

(b) Draw screen plots of both candles on the same axes. Make a copy of the plots below. A labelled “sketch” style copy, showing intercepts, is sufficient.

 

 

 

 

 

 

 

 

 

 

(c) What is the intersection point of the two graphs, and what does it represent? Then confirm it by using algebra below.

 

 

 

 

 

 

 

 

 

(d) Which candle is extinguished first? How much longer does the superior candle last? Where can this length of the time be read on your sketch from part (b) above?

 

 

 

 

 

 

 

 

 

 

(e) If a “Birthday Bash” candle costs $1.80 and an “Intimate Moments” candle costs $2.20, which represents best value for money as far as burning life is concerned? Show your workings.

Subject Mathematics
Due By (Pacific Time) 02/27/2015 12:00 am
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