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Answer:
[tex]f(t) = 15 -1.2t[/tex]
[tex]0 \le t \le 12.5[/tex]
[tex]15 \ge f(t)t \ge 0[/tex]
The length of the candle (in inches) 3.6 hours after it was lit is 0.95 inches
Step-by-step explanation:
Given
[tex]a = 15[/tex] ---- candle length
[tex]r =- 1.2[/tex] --- rate (it is negative because the candle length reduces)
Solving (a): The function, f(t)
This is calculated as:
[tex]f(t) = a + rt[/tex]
So, we have:
[tex]f(t) = 15 + -1.2 * t[/tex]
[tex]f(t) = 15 -1.2t[/tex]
Solving (b): The domain
The domain, in this case, represents time from 0 till the candle burns out.
Set [tex]f(t) = 0[/tex] to calculate the time the candle burns out
[tex]f(t) = 15 -1.2t[/tex]
[tex]0 = 15 - 1.2t[/tex]
Collect like terms.
[tex]1.2t = 15[/tex]
Solve for t
[tex]t = 15/1,2[/tex]
[tex]t = 12.5[/tex]
Hence, the domain is: [tex]0 \le t \le 12.5[/tex]
Solving (c): The range
The domain, in this case, represents the candle height from 15 till the candle burns out (0 inches)
Hence, the range is: [tex]15 \ge f(t)t \ge 0[/tex]
Solving (d): [tex]f(t) = 3.6[/tex]
Recall that:[tex]f(t) = 15 -1.2t[/tex]
Sp, we have
[tex]15 - 1.2t - 3.6[/tex]
Collect like terms
[tex]12t =15 -3.6[/tex]
[tex]12t =11.4[/tex]
Divide by 12
[tex]t =0.95[/tex]