
Rates of Change
I have a math problem that I’m working on that I could use some help with. The question is one to do with decreasing concentrations of a drug in blood over time. I’ve made up some data below to model it out so that I can understand how it’s done –
Time (hrs), Concentration (units)
0.5, 150
1.0, 130
1.5, 115
2.0, 102
The question is  At what time will the rate of decrease in concentration be less than 10 units/hour?
What I’ve done so far is created a graph where I’m charting the log of the time (in mins) against the log of the concentration so that I could determine the gradient. From that I derived an equation to try and use the second derivative to get the rate of change equation but I’m stuck at that point and not sure whether I was even on the right track to begin with.
I’d really appreciate some help.
Thanks.