I did an experiment where I had to measure how fast water flowed out of a container at different times and with different volumes (from 0mL-1000mL in increments of 50). I also had to record the values into a table and graph them. (I got an exponential function).

I got a slope of 0 for the initial instantaneous rate of flow at t=0. How would I answer the following questions?

1. Investigate whether or not the rate of flow will meet the required specifications:

a) when the container is half full.
b) when the container is a quarter full

what specifications? what were the measurements?

The only info I have is when the container is half full which is 500mL in 32.7 seconds and quarter full is 250mL in 23.8 seconds.

To investigate whether or not the rate of flow meets the required specifications when the container is half full or a quarter full, you will need to use the exponential function you obtained from graphing the data.

1. For the container being half full, you will need to find the corresponding volume value of halfway between your minimum and maximum volume values (in this case, halfway between 0 mL and 1000 mL). Let's say this volume is V_half. Once you have V_half, substitute it into your exponential function and solve for the flow rate. This will give you the rate of flow when the container is half full.

2. Similarly, for the container being a quarter full, you will find the corresponding volume value of a quarter of your maximum volume value (in this case, a quarter of 1000 mL). Let's call this V_quarter. Substitute V_quarter into your exponential function and solve for the flow rate, which will give you the rate of flow when the container is a quarter full.

Keep in mind that the exponential function you obtained from your experiment may not necessarily be accurate for extreme values outside of your data range. Therefore, it is important to exercise caution and use your judgment when interpreting the results for volumes that are significantly different from the volumes you tested.