Question

Time(h)Length (in.)Red Blue1Candles. Janis lightstwo candles at the sametime. The red candle is12 in. long and burns atthe rate of 2.5 in./h. Theblue candle is 9 in. longand burns at the rate of1.5 in./h. Show howeach candle's length isa function of the numberof hours the candle hasburnedEquations:23456

Answer 1

To find the function that corresponds to the length of the candle at each hour, fill in the given table, starting by the original lengths of the candles and substracting the corresponding burning rate each time.

Now, use these values to find the equation of each function.

Red. Find the slope using 2 ordered pairs.

$m=\frac{9.5-12}{1-0}=-2.5$

The slope is -2.5 and the y intercept is 12 which is the original length of the candle:

$y=-2.5x+12$

Blue. Do the same procedure with values for the blue candle.

$m=\frac{7.5-9}{1-0}=-1.5$

The equation of the blue candle is:

$y=-1.5x+9$