The Newton`s law of cooling:
T = R + ( To - R ) * e ^(-kt )
We know that: T = 32° F ( the water freezes at 32° F ), To = 55° F, R = 5° F
and the cooling rate is: k = 0.012.
33° F = 5° F + ( 55° F - 5° F ) · 2.72^(-0.012 t )
33 - 5 = 50 · 2.72^(-0.012 t)
27 = 50 · 2.72^(-0.012 t)
2.72^(-0.012 t) = 27/50
1 / 2.72^(0.012 t) = 0.54
2.72^( 0.012 t ) = 1 : 0.54 = 1.85
0.012 t = log(base e) 1.85 = ln 1.85 = 0.6
t = 0.6 : 0.012 = 50
Answer: It would take 50 minutes.
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So, the first five terms of the sequence defined by the given recursive function are shown below.
F(1) 0.75 f(2) 1.1 F(3) 1.45 F(4) 1.8 f(5) 2.15
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Answer:
1. 188.57 meters 2. 1254.20 metres
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