Continuous Exponential Growth Model

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 16% per day. Find the mass of the sample after three days if there were 45 grams of the substance present at the beginning of the study.

Do not round any intermediate computations; round answer to the nearest tenth.

Answer 1

A(t) = A₀e^rt

For this case, A₀=45, r = .16

A(3) = 45e^.16(3) = 45e^.48 = 45(1.6160744020) = 72.7 grams