# Algebra

A scientist 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 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 = 1 to n = 5, and what does it represent? (4 points)

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1. f(n) = 10(1.02)^n

A:
since f(0) = 10, we're looking for a growth of 11.04/10 = 1.104
1.104/.02 is about 50, so as a rough guess I'd go with a domain of [0,50].

B: y-intercept is the initial population (when n=0)

C:
(f(5)-f(1))/(5-1) = 0.21
Represents a constant growth of .21cm/day, on average.

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posted by Steve

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