Question

Please Help!
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

I apologize in advance if the connection times out. If you type a message and I don't reply, please wait. My net connection is horrible and it sometimes says I am typing but I'm not.

Answer 2

Hi Antrod, what's your question? Where are you stuck?

Answer 3

\[f(n)=12(1.03)^n\]is what the growth function really looks like, right?

Answer 4

Yes. Yes. Thats what it looks like.

Answer 5

Thank you so much for staying!

Answer 6

Great. It wouldn't make sense as you typed it — could just have written \[f(n)=12.36n\]if it was all multiplication, and many growth formulas have an exponential form.

So, now that we know what the formula is, what has you stuck?

Answer 7

stupid OpenStudy formatting bug...

Answer 8

The whole question. I know that is all starts from A. How do we answer A? If it says I'm typing after I send this, I'm not.

Answer 9

Okay, so part A is just asking for a reasonable range of values (of \(n\)) to plot the function to include the point where \(f(n) = 16.13\).

Answer 10

do you understand the concepts of domain and range of a function?

Answer 11

Okay. So what d we have to do?

Answer 12

I asked you a question...

Answer 13

Still there?

Answer 14

Sorry. The net messed up. I sent the message of what do we do and I didn't see your question. Answering it now.

Answer 15

yes. x is the domain and y is the range.

Answer 16

I am, still waiting for you to answer my question about whether or not you understand the concepts of domain and range of a function.

Answer 17

okay, good. sometimes it is open study that puts the messages up out of order...

so we know the function, and we know a value of \((x,y)\) of interest. Uh, we know a value of \(y\), we do not know the corresponding value of \(x\), yet. First step is to find the value of \(x\) that gives us that value of \(y\). How would you do that?

Answer 18

I did. x is the domain and y is the range. when there is more than one matching domain its not a function.

Answer 19

12 divided by both sides?

Answer 20

\[f(n) = 12(1.03)^n\]\[f(n) = 16.13\]\[16.13=12(1.03)^n\]\[\frac{16.13}{12} = \frac{12(1.03)^n}{12}\]\[1.344\approx 1.03^n\]
\[n\approx\]

Answer 21

try a few values in your calculator, and find one that gives you something less than 1.344, and something greater.

Answer 22

Or, you could use your knowledge of exponents or logs to find \(n\) directly.

Answer 23

I think I figured it out. Thanks.

Answer 24

Trying to give a medal to you.

Answer 25

once you have figured out values that will let you plot a section of the function that shows it going through the value 16.13, that's your domain for part A.

for part B, think of what the graph represents at \(n=0\). remember that \(n\) is the number of days of growth.

for part C, the average rate of change of a function \(f(x)\) between points \(x=a\) and \(x=b\) is simply \[\frac{f(b)-f(a)}{b-a}\]