{Use of Tech} Flow from a tank A cylindrical tank is full at...

Question

{Use of Tech} Flow from a tank A cylindrical tank is full at time t=0 when a valve in the bottom of the tank is opened. By Torricelli’s law, the volume of water in the tank after t hours is V=100(200−t)², measured in cubic meters.
a. Graph the volume function. What is the volume of water in the tank before the valve is opened?

a. Graph the volume function. What is the volume of water in the tank before the valve is opened?

Accepted Answer

Welcome back, everyone. In this problem, a container is leaking oil, and the volume of oil left in the container after T days can be modeled by the function V equals 200 multiplied by 90 minus T2, where V is measured in liters. Graph the volume function using a graphing utility and calculate the initial volume of oil in the container before it started to leak. Now there are two parts to this problem. First, we'll need to graph the volume function using a graphing utility, and then we can calculate the initial volume of oil before it started to leak. Let's first graph it to get a sense of what our graph looks like. So that's V equals 200 multiplied by 90 minus T squared. So when you're putting this into your graphing utility, remember that T would be the dependent variable and V would be the independent variable like you can see here on our blank graph. Now I'll leave that up to you, but when you do that, it's, it should look something like this, this one that I am pasting on or a screen, OK? So this is going to show the graph of V of T or V as a function of T. Now from this graph, what do we notice? Well, essentially what's happening here is that we have our leak that's started and then our leak is, well, as the days increase, the volume that's left in the container is decreasing, OK? So if we want to find the initial volume of oil, basically we're trying to find the volume when T equals 0. And know when T equals 0, we can find that either by looking at the graph or or plugging 0 into our function. Let's plug 0 into the function. When T equals 0, V equals 200 multiplied by 90 minus 0 squared, OK. And when we work that out, that would be equal to 1,620,000 L. Thus, 1,620,000 L is the initial volume of oil in the container before it starts to leak. Thanks a lot for watching everyone. I hope this video helped.

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