could you please label this as in which questions you are answering (a,b,c,d,e..)! I am getting so confused
I'll copy paste the response with headings Hey Julia! Welcome to the forums!
Question AThe first part is pretty straight forward, and I'm not sure how to construct a table on the forum. Basically, the quantity will decrease over time by 25% every 40 minutes. If t is minutes, and Q is in mg,
etc.
Question BNow, we want to find an equation for Q. We know that what we're looking for here is some sort of
exponential function. Once you've done these questions a number of times, you'll know that the form of the answer must be
Now, we know that the initial quantity is 300mg. So
We also know that the quantity has dropped to 225mg after 40 minutes. So,
So, the equation for the quantity of the medicine is
Question D (C Skipped)Next, we want to find the time it takes for the quantity of medicine to half. I won't bother guessing and checking, let's just find the actual answer.
Remember that this is in minutes. So, dividing by 60, we get t=9.04 hours.
Question EPart e starts to get tricky. We could use an arbitrary time t=a. However, it's exactly the same thing to start at an arbitrary quantity, A. That is because, at time t=a, there will be some quantity A of medicine in the system. Then, we would look for when A halves!
is our new formula. t is still arbitrary, but so is A. Now, we need to show that, regardless of A, the halving time of this equation is a constant (ie. the time we proved in part d).
Our halving time will occur when the quantity is 0.5A (half of the initial, arbitrary amount). So,
But this is exactly the same equation as above, with the same solution! So, the halving time is a constant for any arbitrary starting point.
Question FThe next part is just a standard sketch of an exponential function. If you're not sure what it will look like, plot some points, or use an online graphing tool.
Question GFor the last part, we solve for
Which equals 50.99 hours. We should definitely round up, for the safety of the patient, giving us 51 hours.