Logarithmic and Exponential Growth Practice

Logistic and Exponential Growth Practice 1) Suppose you are in charge of stocking a sh pond with sh for which the rate of population growth is modeled by the differential equation dP = 8P 0.02132 . dt (a) Given P(0) = 50. [i] Find lim P(t). 1)00 (ii) What is the range of the solution curve? [iii] For what values of P is the solution curve increasing? Decreasing? (iv) For what values of P is the solution curve concave up? Concave down? [v] Where does the solution curve have an inection point? 2. The rate at which a rumor spreads through a high school of 2000 students can be modeled by the differential equation dP = 0.003P(2000 P) . where P is the number of students dt who have heard the rumor t hours after 9AM. (a) How many students have heard the rumor when it is spreading the fastest? 3. In a certain national park, the population growth of bears can be modeled by the logistic differential equation 031' E = 0.1P 0.001P2 , where t is measured in years. a) What is the maximum number of bears the national park can hold? b] for what value of P is the population of bears growing the fastest? 4) [From the 1998 BC Multiple Choice] The population P(t) of a species satises the logistic differential equation (ffP = P[2 ] , where the t initial population is P(0) = 3000 and t is the time in years. What is lim P0)? tmo (A) 2500 (B) 3000 [C] 4200 [0) 5000 [E] 10,000