Analyze and evaluate knowledge within the major area. a. Demonstrate computational skills using elements of the real number system. b. Collect, organize and evaluate real number data. c. Demonstrate...

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Answer To: Analyze and evaluate knowledge within the major area. a. Demonstrate computational skills using...

David answered on Dec 22 2021
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Analyze and evaluate knowledge within the major area.
a. Demonstrate computational skills using el
ements of the real number system.
Solution: The first order differential equation is used in many ways in real world. Here, we will
take example of Newton’s empirical law used for cooling/ warming law. For example, when a
chicken is removed from an oven, its temperature is measured as 300
0
F. Three minutes later its
temperature is 200
o
F. Now we can calculate how long will it take for the chicken to cool off to a
room temperature of 70
o
F?
T(t) = Tm+c2e
t

Tm = 70 and T=300 at for t=0.
T(0)=300=70+c2e
.0
This gives c2=230
For t=3, T(3)=200
Now we put t=3, T(3)=200 and c2=230 in (4.1) then
200=70 + 230 e
.3
230
1303 e
Or
23
13
ln3 
Or 19018.0
23
13
ln
3
1

Thus T(t)=70+230 e
-0.19018t
(4.2)
We observe that (4.2) furnishes no finite solution to T(t)=70 since ...
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