How do you graph exponential decay?
Answers
Exponential word problems almost always work off the growth / decay formula, A = Pert, where "A" is the ending amount of whatever you're dealing with (money, bacteria growing in a petri dish, radioactive decay of an element highlighting your X-ray), "P" is the beginning amount of that same "whatever", "r" is the growth or decay rate, and "t" is time. The above formula is related to the compound-interest formula, and represents the case of the interest being compounded "continuously".Note that the variables may change from one problem to another, or from one context to another, but that the structure of the equation is always the same. For instance, all of the following represent the same relationship:
A = Pe^rt ...or... A = Pe^kt ...or. Q = Nekt ...or... Q = Q0e^kt
...and so on and so forth. No matter the particular letters used, the green variable stands for the ending amount, the blue variable stands for the beginning amount, the red variable stands for the growth or decay constant, and the purple variable stands for time. Get comfortable with this formula; you'll be seeing a lot of it.