A question about converting a number into time.

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Rumor

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I wasn't sure which category of math this question would fit into, so I'll just post it here. I just recently finished solving two problems for my calculus class, but I have to convert my answers back into time, and my brain has died and refuses to give me the answer. So I'm turning to you guys. =P

So in the first question, the information looks like this:

Colony weight:
15 mg at 9:00 A.M.
25 mg at 11:30 A.M.
45 mg at ?

where t=0 corresponds to 9:00 A.M. and t=2.5 corresponds to 11:30 A.M. Well, I got t=5.38 as my answer, but I'm unsure as of what time that would be in relation to the data.

The same goes for the second problem.

The information looks like this for the second problem:

Temperature:
34 degrees C at 5:00 P.M.
31.7 degrees C at 7:00 P.M.

where t=0 corresponds to 5:00 P.M. and t=2 corresponds to 7:00 P.M. For this one, I got t=-2.379.

Any help would be appreciated.
 
Rumor said:
… t = 0 corresponds to 9:00 A.M. and t = 2.5 corresponds to 11:30 A.M. Well, I got t=5.38 as my answer, but I'm unsure as of what time that would be …
Click to expand...


There is no way for me to verify your 5.38 result, but, if you're confident that 5.38 is correct, then it means 5.38 hours after 9 AM.

How many minutes is 38/100ths of an hour? Well, it's 38% of 60 minutes.

0.38(60) = 22.8 minutes

In other words, 5.38 hours is roughly 5 hours and 23 minutes. Adding that amount of elapsed time to 9 AM gives 2:23 PM.

On the second exercise, are you sure that your calculated value for t is supposed to be negative (i.e., it represents a time-of-day prior to 5 PM) ?

(You did not explain this exercise, either, so I have no idea.)

Again, if you're confident that t = -2.379 is correct, then finding the corresponding time-of-day works the same way as above.

2.379 hours is 2 hours plus 37.9% of 60 minutes.

0.379(60) = 22.74 minutes

Subtract 2 hours and 23 minutes from 5 PM, to get the time-of-day corresponding to t = -2.379

Both of these exercises look funky, to me. I'm not confident that either of your results for t are correct. :?

 
Re:

mmm4444bot said:
Rumor said:
… t = 0 corresponds to 9:00 A.M. and t = 2.5 corresponds to 11:30 A.M. Well, I got t=5.38 as my answer, but I'm unsure as of what time that would be …
Click to expand...


There is no way for me to verify your 5.38 result, but, if you're confident that 5.38 is correct, then it means 5.38 hours after 9 AM.

How many minutes is 38/100ths of an hour? Well, it's 38% of 60 minutes.

0.38(60) = 22.8 minutes

In other words, 5.38 hours is roughly 5 hours and 23 minutes. Adding that amount of elapsed time to 9 AM gives 2:23 PM.

On the second exercise, are you sure that your calculated value for t is supposed to be negative (i.e., it represents a time-of-day prior to 5 PM) ?

(You did not explain this exercise, either, so I have no idea.)

Again, if you're confident that t = -2.379 is correct, then finding the corresponding time-of-day works the same way as above.

2.379 hours is 2 hours plus 37.9% of 60 minutes.

0.379(60) = 22.74 minutes

Subtract 2 hours and 23 minutes from 5 PM, to get the time-of-day corresponding to t = -2.379

Both of these exercises look funky, to me. I'm not confident that either of your results for t are correct. :?

Click to expand...
Yes, I am sure that the value for t in the second portion is supposed to be negative.

For both of these problems, the objective was for me to figure out the time; for the first one, the time where the colony weight is 45mg and for the second one, at what time it was when the temperature was 37 degrees C (since it was decreasing).

For the first one, the equation to be used was of exponential growth, y=y0e^kt and for the second, Newton's Law of Cooling: T(t)=Se^(-kt) + M where M=20 degrees C. Although I'm a little sketchy on this second problem, I believe my answer is at least in the right direction.

So that's the basis of the problems.
And thank you for your help. :]
 
Rumor said:
I wasn't sure which category of math this question would fit into, so I'll just post it here. I just recently finished solving two problems for my calculus class, but I have to convert my answers back into time, and my brain has died and refuses to give me the answer. So I'm turning to you guys. =P

So in the first question, the information looks like this:

Colony weight:
15 mg at 9:00 A.M.
25 mg at 11:30 A.M.
45 mg at ?

where t=0 corresponds to 9:00 A.M. and t=2.5 corresponds to 11:30 A.M. Well, I got t=5.38 as my answer, but I'm unsure as of what time that would be in relation to the data.

The same goes for the second problem.

The information looks like this for the second problem:

Temperature:
34 degrees C at 5:00 P.M.
31.7 degrees C at 7:00 P.M.

where t=0 corresponds to 5:00 P.M. and t=2 corresponds to 7:00 P.M. For this one, I got t=-2.379.

Any help would be appreciated.
Click to expand...

I'll do a similar, but different quick example.

What time is it when it's 3.7 hours past 8 a.m.?

3.7 hours = 3 hours + .7 hours
There are 60 minutes in an hour, so .7 hours is .7 * 60 minutes, or 42 minutes

So, 3.7 hours = 3 hours 42 minutes

Add that to 8 a.m., and you get (8 + 3) hours 42 minutes....11:42 a.m.

You'll need to be careful when your addition takes you past 12....unless you're dealing with a 24-hour clock.
 
Rumor said:
… So that's the basis of the problems …
Click to expand...


Now that I see the exercises, the situation makes sense, to me.

I get a different value for t, on the second exercise.

My answer is roughly 2:50 PM.

(I used S = 14 and M = 20.) 8-)

 
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