I'm brand new to calculus and am hoping for some insight into probably a very basic problem. The question is as follows:
"A cylindrical tank holds 100,000 gallons of water, which can be drained from the bottom of the tank in an hour. The graph shows the volume of water, y, left in the tank after x minutes."
Followed by this graph: Graph
Then it goes on to ask:
"At what time is the volume decreasing at a rate of 2000 gallons per minute?"
I could build a chart with approximate data based on the chart and then get a rough estimate that way, but is there a better way? No formulas or data are given, only the graph. Is there a way to get an exact answer? Sorry if this is an easy question, or if I phrased the title wrong, I've just been out of school for a while and am a bit confused.
The graph looks kind of like a reciprocal function? So that could be helpful in finding an answer, if I knew exactly what the function was. Could I figure out the function based on the data given? Thanks in advance for any insight!
Like @MohammadZuhairKhan noticed, your the flow rate is the slope of the tangent to your graph at a given point, therefore you can write the equation of the tangent as $y=-2000 \rm{gal/min}\cdot t+c$. That $2000 \rm{gal/min}$ you can show on the graph as a line that intersects the vertical axis at $20000\rm{gal}$ and the horizontal axis at $10\rm{min}$. Now you just need to draw a parallel to this line that is tangent to the graph. You obtain one at intersections of about $50000\rm{gal}$ on the vertical axis and $25\rm{min}$ on the horizontal. The tangent point intersects the curve at $t=15\rm{min}$