1) What is a key characteristic of exponential growth? a) It increases by the same amount each step b) It forms a straight line on a graph c) It grows faster and faster as time goes on. d) It eventually reaches a maximum value. 2) What is the base in the exponential function f(x) = 3 . 4x a) 3 b) 4 c) X d) 3X 3) Which of the following correctly describes the graph of an exponential growth function f(x) = 2⋅(3)x ? a) It has a horizontal asymptote and increases slowly at first, then more rapidly. b) It forms a straight line with a positive slope. c) It decreases over time, approaching zero but never reaching it. d) It has a vertical asymptote and increases at a constant rate. 4) How does changing the base of an exponential function affect its graph? Given the functions f(x)=2⋅(3)x and g(x)=2⋅(5)x: a) Both graphs show exponential growth, but g(x) grows faster because its base is larger. b) Both graphs show exponential decay, but g(x) decays more slowly because its base is larger. c) The y-intercepts are different, causing the graphs to start at different points. d) f(x) and g(x) both decrease over time because their bases are greater than 1. 5) A rare species of plant is introduced to an ecosystem and its population is modeled by the function P(t)=200⋅(1.25)t , where t is the number of years since introduction. Predict what will happen to the population after a long period of time, and explain the behavior of the graph. a) The population will grow rapidly and without bound because the growth rate is greater than 1. b) The population will level off at a maximum limit because of environmental constraints. c) The population will decrease after a few years, as the growth rate stabilizes. d) The population will fluctuate up and down due to changes in environmental factors.

EXPONENTIAL FUNCTION

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