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)

Question

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)

mertsj · Answer

Well, if n is the number of days, what do you think would be a good choice for replacements for n?  I probably wouldn't use sqrt2 or pi or 1.64, would you?

anonymous · Answer

So what about 1, 2, 3 , 4, and 5?
Since it's days.

mertsj · Answer

Seems sensible to me.  We might want to be more flexible and say "the counting numbers".

anonymous · Answer

So would the y intercept represent the height of the plant ?

mertsj · Answer

Yes.  At day 0 or in other words, at the beginning of the experiment.

anonymous · Answer

What would the rate of change represent ?
The growth rate of the plant ?

mertsj · Answer

The rate of change is just what it says.  The rate the height of the plant is changing.  Since it is an average rate of change, it would be the average change per day over the length of the study.