A 11-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let t represent the number of hours since the candle was lit, and suppose f is a function such that f (t) represents the remaining length of the candle (in inches) t hours after it was lit. Write a function formula for f.

Question

Mathematics

Adrian Fitzgerald

3 March, 18:35

A 11-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let t represent the number of hours since the candle was lit, and suppose f is a function such that f (t) represents the remaining length of the candle (in inches) t hours after it was lit. Write a function formula for f.

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Answers (1)

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Jaylene Hamilton · Answer 1

f (t) = 11 in - 1.3 in/h * t

Step-by-step explanation:

defining the length of the candle as L, then since the candle burns at a constant rate, then

-dL/dt = 1.3 in/h = a

therefore

-∫dL = a∫dt

-L (t) = a*t + C, C=constant

at t=0, the length of the candle is L₀ = 11 in, thus

-L₀=a*0 + C → C = - L₀

replacing the value of C

-L (t) = a*t - L₀

L (t) = L₀ - a*t = 11 in - 1.3 in/h * t

then

f (t) = 11 in - 1.3 in/h * t