3)T(h) is the number of cell phones manufactured by a particular factory each ho

Question

3)T(h) is the number of cell phones manufactured by a particular factory each hour h hours after 8:00 a.m.

a. Would it make sense for T(h) to be negative? Explain. (4 points)

2 points – correct “no” answer 2 points – valid explanation

b. Would it make sense for T'(h) to be negative? Explain. (4 points)

2 points – correct “yes” answer 2 points – valid explanation

c. Interpret the expression 1500 dT dh = . (6 points)

2 points – correct output label 2 points – complete and correct sentence 2 points – correct verb tense

d. What does the statement 100 dT dh = tell you about production? (4 points)

2 points – correctly identify decreasing production 2 points – correctly identify magnitude of decreasing rate

Explanation / Answer

a)

T(h) is the number of phones manufactured
This can never be negative as we cannot manufacture a negative number of cellphones.
So, NO

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b)

T ' (h) is the rate of change of the number of phones manufactured per hr. This can sure be negative because it is possible for the rate of manufacture to decrease over time. Like for example, say at 8 am, the rate was 100 phones per hr and if at 9 am, the rate is 80 phones per hr, then it constitutes a decrease in rate, i.e rate is negative
So, yes, this is possible

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c)

1500 dT dh = .
This is what i see and it makes no sense......
Lets say it was 1500 dT/dh = a

So, dT/dh = a/1500

This tells us that dT/dh is positive, i.e the rate of manufacture of phones is increasing with time and it is increasing at the rate of a/1500 phones per hour.

Now, i have used 'a' here because there was nothing else in your question... In place of 'a', whatever it was, please use that when u write your answer....

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d)

100 dT/dh = -
is what i see for part D, which also seems to be missing a part...
Lets say it was -b on the right...

100dT/dh = -b

So, dT/dh = -b/100

This shows that with time, the rate of manufacture decreases
at rate of b/100 phones per hr. The negative value of dT/dh indicates a decrease and a positive value for dT/dh indicates an increase... So, this tells us that production rate keeps dereasing as time passes.
And the magnitude of decreading rate is b/100 phones per hour

Now, i have used 'ab' here because there was nothing else in your question... In place of 'b', whatever it was, please use that when u write your answer....

Please comment if you have any questions on this answer. All the best!

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