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Calculus Help?

Gamingphreek

Gamingphreek

Lifer
Yeah, im supposed to know this seeing as i took AP Calculus in HS, but i dont. Thats why i retook Calculus 1205 in College. I thought i would be able to learn it better, but i got a teacher that barely speaks English! So I was desperately trying to understand how to do everything but i couldn't. Now on my HW im having problems.

If someone could just guide or prompt me through this one problem that would help immensely.

1) A tank holds 1000 gallons of water, which drains from the bottom of the tank in half and hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.

t: 5||10 ||15 ||20 ||25||30||
V:694||444||250||111||28|| 0||

If P is the point (15,250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t=5,10,20,25,30.

Once again i feel really ashamed for asking this because it is probably insanely simple for you guys (and it should be for me). I dont need the answer or for someone to do it for me, i just need someone to guide me through this one problem.

-Kevin
 
Oh dear god. Do i find this the same way i would find the slope of any other line.

Since i know P is (15,250) and i know Q1 is (5,694). So is it merely (694-250)/(5-15)?

-Kevin
 
I also took AP calc this past year in HS. I believe the problem is ultimately asking you to estimate the instantaneous rate of change at t=15. To do this, you need to find the slopes of the secant lines around t=15, and see what number they approach. It may be easier to visualize and do this if you make a graph using those given points.

edit: yes, that's how you would find the slope of the first secant line. Do that for the rest of them.
 
Oh man. I used to love these problems. However, it's been 3 years since I took AP BC Calc and I've forgotten how to do that. Here's a free bump! And to think, I just switched to Secondary Ed - Mathematics! Luckily I'm sitting in on a calc class this semester.
 
Haha, well so far i the problem is working out. It definitely was merely (Y2-Y1)/(X2-X1). Now i feel stupid lol.

If i have any more problems ill post back, but i have a Calc class in 30 mins.

-Kevin
 
OMG I hated changing rates of crap, never could figure it out. Have fun with this.

Oh btw, now you know how I almost failed CS class.
 
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