= O Given a starting estimate of to 0 hours, use a single iteration of Newton's method to approximate the value of t where the thermic effect of food above resting metabolic rate, T(t), first reaches 40 kJ·h¯¹. Note: T'(t) = 175.9e-t/1.3 (1-13).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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do question b only

Thermic effect of food above RMR (kJ⋅h¯¹)
80
60
40
20
h 5-
bt
6
0
1
2
4
5
6
3
Time (h)
Figure 3. Model of thermic effect of food above resting metabolic rate over time
(adapted from [5]).
(a) Using the trapezoidal rule with hourly increments, approximate the area under the curve
of T(t) on the interval 0 ≤ t ≤ 6 given the following data points:
1
2
t (h) 0
T (kJ.h−¹)| 0.0
3 4 5 6
75.5 52.5 32.4 18.8 10.4
81.5
Transcribed Image Text:Thermic effect of food above RMR (kJ⋅h¯¹) 80 60 40 20 h 5- bt 6 0 1 2 4 5 6 3 Time (h) Figure 3. Model of thermic effect of food above resting metabolic rate over time (adapted from [5]). (a) Using the trapezoidal rule with hourly increments, approximate the area under the curve of T(t) on the interval 0 ≤ t ≤ 6 given the following data points: 1 2 t (h) 0 T (kJ.h−¹)| 0.0 3 4 5 6 75.5 52.5 32.4 18.8 10.4 81.5
(b) Given a starting estimate of to = 0 hours, use a single iteration of Newton's method to
approximate the value of t where the thermic effect of food above resting metabolic rate,
T(t), first reaches 40 kJ.h−¹. Note: T'(t) = 175.9e-t/¹.³ (1 – 13).
t
Transcribed Image Text:(b) Given a starting estimate of to = 0 hours, use a single iteration of Newton's method to approximate the value of t where the thermic effect of food above resting metabolic rate, T(t), first reaches 40 kJ.h−¹. Note: T'(t) = 175.9e-t/¹.³ (1 – 13). t
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