Applications of Derivative (Exponential Growth and Decay)

( D) amount. The population of two countries, Stavland and Vouland can be modeled by 6. S = 30000e02 and V = 10000e0. respectively. According to these models, what is the combined population of Stavland and Vouland after ten years? (a) after how many years will the populations of the two countries be equal? (b) (c) when will the populations be increasing at the same rate? 7. The mass, M grams, of a radioactive substance after t years is given by M = 800e-0.0003: (a) Calculate the mass of the substance after 10 years. (b ) Find the average rate of decrease in grams per year of the substance over the first 10 years. (c) (i) Sketch a graph of the rate of change of the mass against time. (ii) Use the graph to find the rate of decrease of the substance after 10 years. (iii) Check your answer to part (ii) algebraically. 8. The value of an antique table purchased Terry for $10 000 in January 1990 is expected to appreciate according to the model P = Pe , where t is the time in years since the table was purchased. (a) How much will the table be worth after 10 years? (b) At what rate will the value of the table be increasing after 10 years