Question

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?

Answer 1

@SolomonZelman

Answer 2

@texaschic101

Answer 3

I got disconnected, I am really sorry _:(

Answer 4

its fine

Answer 5

\(\LARGE\color{blue}{ \bf f(n)=12(1.03)^{n} }\) is the function, where f(n) represents the height of the plant, and n represents the day(s).

you know that the height of the plant is 16.13, plug that instead of f(n)

\(\LARGE\color{blue}{ \bf 16.13=12(1.03)^{n} }\)

can you solve for n?
( Just curious, is this algebra 1 ? )

Answer 6

yes, it is

Answer 7

then I don't think you will be able to get an EXACT answer, however you can estimate it, but hardly.

If I show you the exact solution I am not sure if you get it, but do you want to try it?

Answer 8

yes

Answer 9

I will try it

Answer 10

10.006299982393

Answer 11

?

Answer 12

\(\LARGE\color{blue}{ \bf 16.13 =12(10.3)^{n}}\)
divide both sides by 12, and I get,
\(\LARGE\color{blue}{ \bf 1.34 =(10.3)^{n}}\) now, I am hitting both sides with a log,

\(\LARGE\color{red}{ \bf log~1.34 =log~(10.3)^{n}}\) now I am simplifying the log,

\(\LARGE\color{red}{ \bf log~1.34 =n ~log~(10.3)}\)

\(\LARGE\color{red}{ \bf log~1.34~~/~~log~(10.3) =n ~}\)

\(\LARGE\color{red}{ \bf log~_{(10.3) }1.34=n ~}\)

\(\LARGE\color{red}{ \bf n=0.13 ~}\)

Answer 13

Well, I think the domain would then be approaching zero.

Answer 14

okay

Answer 15

What does the y-intercept of the graph of the function f(n) represent?

Answer 16

the y-intercept, is when n equals zero.
So, if n=0 that means that no days have passed, or in other words, it is the initial height of the plant.

Answer 17

uh... isn't it 1.03 and not 10.3?