Hey,Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem.
When doctors prescribe medicine, they must consider how much the drug’s effectiveness will decrease as time passes. If each hour a drug is only 95% as effective as the previous hour, at some point the patient will not be receiving enough medicine and must be given another dose. If the initial dose was 250 mg and the drug was administered 3 hours ago, how long will it take for the initial dose to reach a dangerously low level of 52 mg? First, we will need to use the general exponential decay formula: which u must know In the formula, represents the amount of medicine after time has passed. represents the initial amount of medicine. The constant a represents the rate of decay (and is always a number between 0 and 1), and t stands for time, which is in hours in this problem. Now, we need to substitute known values for the variables in the formula. The problem asks how long it will take the initial dose to become dangerously low. Therefore, is 52 in this problem. is the initial dose which is 250 mg. The rate of decay is which will be converted to the decimal 0.95. Time t is what we are trying to find. So we have the following: