Ascientist is studying the growth of a particular species of plant. he writes the following equation to show the height of the plant f(n), in cm, after n days: f(n)= 10(1.02)^n part a) when the scientist concluded his study, the height of the plant was approximately 11.04 cm. what is a resonable domain to plot the growth function? part b) what does the y-intercept of the graph of the function f(n) represent? part c) what is the average rate of change of the function f(n) from n=1 to n= 5, and what does it represent?

F(n) = 10(1.02)^n part a) when the scientist concluded his study, the height of the plant was approximately 11.04 cm. what is a resonable domain to plot the growth function? f(n) = 10 (1.02)^n = 11.4=> (1.02)^n = 11.04 / 10=> (1.02)^n = 1.104=> n log(1.02) = log (1.104)=> n = log (1.104) / log (1.02) = 4.996 so, a reasonable domain is [0, 5] < answerpart b) what does the y-intercept of the graph of the function f(n) represent? the y-intercept of the graphs of the function f(n) is the value of the function when n = 0, f(0), so it represents the initial (start) height of the plant (when the study started).part c) what is the average rate of change of the function f(n) from n=1 to n= 5, and what does it represent? n = 1 => f(1) = 10(1.02) = 10.2 cmn = 5 => f(5) = 11.04 cmaverage rate of change of the function = [ f(5) - f(1) ] / [5 - 1]average rate of change = [11.04 cm - 10.2 cm] / [4 day] = 0.21 cm/dayanswer: 0.21 cm/day