Calculus

I did an experiment where I had to measure how fast water flowed out of a container at different times and with different volumes. I also had to record the values into a table and graph them. (I got an exponential function). I am to answer the following questions and I do not know how to answer them:

1. a) What connections can you make between instantaneous flow rates at a specific time and tangents to the graph?

b) Approximate the instantaneous rate of flow, when 750 mL of water has been collected in the measuring cup, by using your graph and a series of secants containing the point.

I don't understand what is meant by a series of secants.

2. a) Specifications for the water tower require that the rate of flow cannot be less than half the initial instantaneous flow rate. What is the initial instantaneous rate of flow (the rate of flow at the start of the experiment)?

would this be the average rate of water flow over the whole time interval?

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asked by Liz
  1. secants connect two points on the graph. The slope of the secant is the average rate of change during that interval.

    The tangents are just secants where the interval has zero length -- their slopes are the instantaneous rates of change.

    The initial instantaneous rate is just the slope of the tangent at t=0.

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    posted by Steve

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