Question

Would you help me with 64 A, B , and C i

Answer 1

Given data:

Rate of decrease: 2.5 inches per hour

After 1.5 hours the candle is 11.5 in long

Let x be the number of hours

Let y be the length of the cangle remaining

Linear equation:

`\begin{gathered} y=mx+b \\ \\ m=rate\text{ of change} \\ b=initial\text{ value} \\ \\ \\ y=-2.5x+b \end{gathered}`

Use given data to find b: After 1.5 hours the candle is 11.5 in long

x=1.5

y=11.5

`\begin{gathered} 11.5=-2.5(1.5)+b \\ 11.5=-3.75+b \\ 11.5+3.75=b \\ b=15.25 \end{gathered}`

a. Formula:

`y=-2.5x+15.25`

b. The formula describes the remaining length (y) using two terms:

-2.5x: first term, this term includes the slope or rate of change (-2.5) and the variable (x)

15.25: second term it the initial lengh of the candle

c.

i. Evaluate the formula for x=3

`\begin{gathered} y=-2.5(3)+15.25 \\ y=-7.5+15.25 \\ y=7.75 \end{gathered}`

After 3 hours burned the length of the candle is 7.75 inches

ii. Evaluate the formula for x=5

`\begin{gathered} y=-2.5(5)+15.25 \\ y=-12.5+15.25 \\ y=2.75 \end{gathered}`

After 5 hours burned the length of the candle is 2.75inches