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Let's do a couple of word problems dealing with exponential growth and decay.So this first problem, suppose a radioactive substance decays at a rate of 3.5% per hour.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.
It was originally used to describe the decay of radioactive elements like uranium or plutonium, but it can be used for any substance which undergoes decay along a set, or exponential, rate.
You can calculate the half-life of any substance, given the rate of decay, which is the initial quantity of the substance and the quantity remaining after a measured period of time.
One quick way to do this would be to figure out how many half-lives we have in the time given.
6 days/2 days = 3 half lives 100/2 = 50 (1 half life) 50/2 = 25 (2 half lives) 25/2 = 12.5 (3 half lives) So 12.5g of the isotope would remain after 6 days.
And then we'll try to come up with a formula for, in general, how much is left after n hours. So in hour 1, we're going to have 96.5% of hour 0, or 0.965 times 100, times hour 0. Well, we're going to have 96.5% of the previous hour.
So let's say hours that have passed by, and percentage left. Well, it hasn't decayed yet, so we have 100% left. We will have lost 3.5%, which means that we have 96.5% of the previous hour.
So over 8 years, you see that the compounding growth by 8% actually ends up being quite dramatic.
Meredith Juncker is a Ph D candidate in Biochemistry and Molecular Biology at Louisiana State University Health Sciences Center.
It is best to work from the inside out, starting with the exponent, then the exponential, and finally the multiplication, like this: Not all algebra classes cover this method.
If you're required to use the first method for every exercise of this type, then do so (in order to get the full points).