The function Ht] 2 500 - 2t is a model for a Population A, where t is measured in years. The function 1.5000 1 + 29 - 2* is a model for a Population B, where f is measured in years. {a} Fill in the table for the functions fancl g for the given values of t. [Round your answer to the nearest whole number.) (b) Are .he initial populations for A and B the same? 0 Yes O No (c) Which population grows exponentially? 0 Population A 0 Population B (d) which population grows logistically? 0 Population A 0 Population B What is the carrying capacity? : The population of a species with limited resources is modeled by a logistic growth function f. Use the graph of {to estimate the initial population and the carrying capacity. initial popuiation :I Y Need Help? The graphs of two population models are shown. One grows exponentially and the other grows logistically. J-i' (a) which population grows exponentially? 0 Population A O Population B (h) 1which population grows logistically? O Population A 0 Population B What is the carrying capacity? E (c) What is the initial population for A and For B? E BOD A population with limited resources is modeled by the logistic growth function for) : x. The initial population is :l , and the carrying capacity is |: . 1 + 24 - 3' Need Help? Some bullfrogs were introduced into a small pond. The graph shows the bullfrog population for the next few years. Msume that the population grows exponentially. Frog population (11) 1200 1000 800 600 [2, 22 5) (D, 100) 400 200 (a) What was the initlal bullfrog population? |:| (b) Find an exponential growth model n[t} 2 Car for the population 1' years since the bullfrogs were put into the pond. n[t} = What is the growth rate? |:| % (c) Use the model to nd the percentage rate of change from t = 2 to t = 3. |:| % Compare your answer to the growth rate from part (b). C) It is higher than the growth rate in part {b}. 0 It is lower than the growth rate in part [b]. 0 It is the same growth rate in part (b). A set of data with equally spaced inputs is given in the table below. Complete the table for the percentage rate of change of the outputs y. Percentage rate X y of change 5 7 15 200% 2 45 3 135 4 405 (a) Since the percentage rate of change ---Select--- v , there is an exponential model f(x) = C . a* that fits the data. (b) The percentage rate of change is the constant %, so the growth rate r is , and the growth factor a is (c) An exponential model that fits the data is f(x) = X Need Help? Read It