A candle is lit and the length of the burning candle changes at a constant rate of -1.7 inches per hour. 3 hours after the candle was lit the candle was 8.3 inches long.

Question

A candle is lit and the length of the burning candle changes at a constant rate of -1.7 inches per hour. 3 hours after the candle was lit the candle was 8.3 inches long.

Write a formula that expresses the remaining length of the candle in inches, , in terms of the number of hours  that have elapsed since the candle was lit.

Answer 1

Since the relationship is linear, the equation for the length (inches) of the candle (L) is

L = -1.7t + L_o where t = time in hours & L_o = the starting length of the candle

To solve for Lo, substitute the information given 8.3 = -1.7(3) + L_o or L_o = 13.4 inches

Therefore,

L = -1.7t + 13.4