Question

A blue candle and red candle are lit at the same time but burn at different rates. The blue candle is 6.5 inches long when lit and burns at a constant rate of 0.55 inches per hour. The red candle is 5.8 inches long when lit and burns at a constant rate of 0.3 inches per hour. The function b gives the length of the blue candle in inches, b ( t ) , as a function of the number of hours t since the candles were lit. The function r gives the length of the red candle in inches, r ( t ) , as a function of the number of hours t since the candles were lit. Write function formulas for b and r .

Answer 1

Function formula for b(t) = 6.5 + 0.55t

Function formula for r(t) = 5.8 + 0.3t

Explanation:

As given,

For b(t) - Blue candle

Length of blue candle = 6.5 inches

Burn rate = 0.55 inches per hour

Now,

b(t) = Burn rate × Time + Length

⇒b(t) = 0.55t + 6.5

∴ we get

Function formula for b(t) = 6.5 + 0.55t

For r(t) - Red candle

Length of red candle = 5.8 inches

Burn rate = 0.3 inches per hour

Now,

r(t) = Burn rate × Time + Length

⇒r(t) = 0.3t + 5.8

∴ we get

Function formula for r(t) = 5.8 + 0.3t