Question

A candle is 6 tall after burning for one hour. After 3 h, it is 5. 5 tall. Write a linear equation to model the hh () of the candle after burning () h.

Answer 1

h(t) = -0.25t + 6.25

Explanation:

Given that :

Height of candle after burning for 1 hour = 6

Height of candle after burning for 3 hours = 5.5

The linear model to show the height ight of candle after burning for h hours :

The height change per hour of burn ; this is the slope ;

Change in height / Change in time ;

Time = 1 hour ; height = 6

Time = 3 hours ; height = 5.5

Slope = (5.5 - 6) / (3 - 1) = - 0.5 / 2 = - 0.25

This means candle height decreases ; - 0.25 ft per hour :

Based on the linear, slope, intercept equation ;

y = mx + c

Candle height, h

h(t) = mt + c

c = intercept, we can obtain this thus ;

Using the height at 1 hour and slope;

After an hour burn :

6 = - 0.25t + c

t = 1

6 = - 0.25(1) + c

6 = - 0.25+c

6+0.25 =, c

c = 6.25

Hence ; to calculate height, h after burn time &

h(t) = -0.25t + 6.25