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) = 8(1.05)^n part a: when the scientist concluded his study, the height of the plant was approximately 11.26 cm. what is a reasonable domain to plot the growth function? (4 points) part b: what does the y-intercept of the graph of the function f(n) represent? (2 points) part c: what is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent? (4 points)

Part A) It depends on how long the experiment will be  the domain must start from zero and should go as long as the experiment will last.

Part B)  y intercept would be the height of the plant after n days

Part C)  8(1.05)^2 = 8.82, 8(1.05)^6 = 10.72

10.72 - 8.82 = 1.9

6-2 =4

1.9 /4 = 0.475

 this means the plant grows at an average of 0.475 cm per day

Part A: The value of n is 7. Thus, the domain of the function is from 0 to 7.

Part B: The y-intercept is 8 and it represents the height of the plant in cm after n days

Part C: By substituting the values of n to the equation the values of f(n) are 8.82, 9.261, 9.72, 10.21,10.72. The average is 9.75. This is the average length of the plant for days 2 to 6.

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