Question

The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. a sample increases continuously at a relative rate of 18% per day. find the mass of the sample after six days if there were 38 grams of the substance present at the beginning of the study.

Answer 1

Then we know that we originally had 38 grams of the substance, the rate of growth is 18%, and that the time it was allowed to grow is 6 days. Then we have using the exponential growth model that the amount of the sample after 6 days will be S = P e^rt where P is the initial sample amount, r is the rate of growth, t is the time, and S is the final sample amount. S = 38 e^ .18*6 = 38 e ^ 1.08 = 111.8978 Thus if there were 38 grams of the substance present at the beginning of the study the mass of the sample would be 111.8978 grams after the study.