Question

Fan and Medal:

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) = 12(1.03)n

Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 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 = 3 to n = 10, and what does it represent? (4 points)

Answer 1

@uri @phi @Australopithecus

Answer 2

plug in 16.13 for f(n) since that's what represents the height and get the height at that day.
And then, I would graph the domain from 0, when planted, till it reached that height. (can't go further, nor into the negatives since days are a positive #).

The y intercept occurs when x, or in this case n, = 0.
On the 0 day I would assume to plant it, so I'd be the initial height.

the average rate of change.
def. of average rate of change: \[\frac{ y _{1}-y _{2}}{ x _{1}-x _{2}}\]

[the #'s would be sub scripts for that definition)
so plug in 3 into the function to get f(3) and 10 to get f(10) and then use the formula.
=
\[\frac{ f(10) - f(3) }{ 10 - 3 }\]

don't forget your units.

Answer 3

Thank you so much

Answer 4

ur welcome...........