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.

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.

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