Time, t Depth, y

Midnight 3.4 (remember midnight = 0 hours)
2 am 8.7
4am 11.3
6am 9.1
8am 3.8
10am 0.1
noon 1.2
If I wanted to find the times at 3 and 9 isnt there a way to do that on my ti-83 or is that a formula?

Question

Time, t Depth, y 
 
 Midnight 3.4 (remember midnight = 0 hours) 
 2 am      8.7 
 4am      11.3 
 6am       9.1 
 8am      3.8 
 10am     0.1 
 noon      1.2
If I wanted to find the times at 3 and 9 isnt there a way to do that on my ti-83 or is that a formula?

anonymous · Answer

9am and 3pm

mathmale · Answer

Mike:  What you're asking is unclear.  What does your table represent?  What do you want to evaluate / find at 9 a.m. and 3 p.m.?  If you'd clarify all this, then perhaps I could be of more help to you.

anonymous · Answer

Yea I want to find the depth at 9am and 3pm.

mathmale · Answer

No function is given, but only points on a supposed curve (graph) representing some unknwon function.  My suggestion wuld be that you graph all fo the points (using Draw, below), and then "connect the dots."  Look up the word "interpolate" by doing an Internet search.

Considering 9 a.m.:  Your table shows that at 8 a.m., the depth is 3.8 feet (or whatever unit applies here, whereas at 10 a.m., it's 0.1 feet.  no depth is given for 9 a.m.  Therefore, we must "interpolate" to estimate what the depth was for 9 a.m.

This is why I wanted you to look up the word "interpolate" and get a good idea of its meaning and the application of this mathematical concept to the problem at hand.  Looking at your sketch would be another way to estimate the depth at 9 a.m.

anonymous · Answer

I believe I have actually done this here is my model y= 5.6 cos (51.43x-154.29) + 5.7 and then I also did a scatter plot and lined them up to look like a interpolate, so is there a way in my calculator to find the value? If I did value and trace and do 2.5 since it is inbetween the times 2 and 3 and got 10.75 is that right?

mathmale · Answer

Mike, sorry, but I didn't know you were working with a cosine function.  Note that you didn't mention either trigonometry or cosine in your problem statement.

I notice that "this question is closed."  I didn't close it; did you?  In any case, if you're still interested in solving this problem using trigonometry, repost the problem in the "Ask a question" box, (not here); then we could get a fresh start, assuming that you want to continue.

anonymous · Answer

I think I solved it correctly thanks for the help!