I am given this data table:

Question

Time After Consumption (min): 30, 60, 90, 120, 150, 180
Amount of Codeine in Blood (mg): 27.0, 23.5, 21.2, 18.7, 16.6, 14.5

Question:
I created a scatter plot of the data. How would I determine an equation to model the amount of codeine in the bloodstream t minutes after taking the pill and justify it?

Answer 1

It might be helpful to rescale things by letting

u = (x-30)/30

so the u-values go from 0 to 5. Then, since we are expecting an exponential relationship, see whether you can find something that fits

∆y/∆u = ky + c

See where that takes you