Exponential & Logistic Equations in Science, Economics, & Population Growth, Study notes of Mathematics

Download Exponential & Logistic Equations in Science, Economics, & Population Growth and more Study notes Mathematics in PDF only on Docsity! MATH 1090 Sec. 5 Section 5.3: Applications Solving exponential equations Ex.1 (#12) Solve the equation for x: 2500 = 600e0.05x Exponential growth/decay models Ex.2 (#86) A breeder reactor converts stable uranium-238 into the isotope plutonium-239. The decay of this isotope is given by A(t) = A0e−0.00002876t where A(t) is the amount of the isotope at time t, in years, and A0 is the original amount. Find the half-life of this isotope. Ex.3 (#88) The population of a certain city grows according to the formula y = P0e0.03t. If the population was 250,000 in 2000, estimate the year in which population reaches 350,000. 1 Economic and management applications Ex.4 (#92) The demand function for a product is given by p = 3000e−q/3. (a) At what price per unit will the quantity demanded equal 6 units? (b) If the price is $149.40 per unit, how many units will be demanded, to the nearest unit? Gompertz curves and logistic functions 1. Gompertz equation: N = CaR t t: time R: a constant that depends on the population (0 < R < 1) a: the proportion of initial growth C: the max possible number of individuals N : the number of individuals at a given time t Ex.5 (#112) A firm predicts that sales will increase during a promotional campaign and that the number of daily sales will be given by N = 200(0.01)0.8 t , where t represents the number of days after the campaign begins. How many days after the beginning of the campaign would the firm expect to sell at least 60 units per day? 2