Question

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 .

Answer 1

Answer:

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