Question

I already have the answer for this, I just need to know what it means.


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) = 15(1.04)n

What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

Answer 1

What does it represent? is the part I need help with.

Answer 2

I was guessing that it represents the slope or the average rate of change. I'm not sure though.

Answer 3

average rate of change of the function f(n) from n = 1 to n = 5
if you draw a line through the points (1, f(1) ) and (5, f(5) )
the slope of that line is the average rate of change

in other words, slope = change in "y" divided by change in "x"
is, for this problem
\[ \frac{ f(5) - f(1)}{5-1} = \frac{ f(5) - f(1)}{4} \]
which is the total change in growth per 4 days, or the "average growth per day"
after we simplify it.

Answer 4

So it represents the average rate of growth, or the change in y divided by the change in x. Right?

Answer 5

yes, but we are not using y's and x's (I mentioned them because that is often how we talk about slope), so maybe it's better to say the change in the function divided by the number of days

Answer 6

Oh okay. Thank you! :D