Question

here

Answer 1

@kittiwitti1

Answer 2

Okay so:
\[f(n)=12(1.03)^n\]
Let n=days
Let f(n)= height of plant in cm

Part A. The height of the plant at the end of the experiment was 16.13cm...
Finding reasonable domain -->

Let 16.13=f(n) & solve for n
\[16.13=12(1.03)^n\]
Solve:
\[\frac{ 16.13 }{ 12 }=1.03^n\]
\[\ln (16.13) - \ln (12) = n \ln (1.03)\]
\[\frac{ \ln (16.13) - \ln (12) }{ \ln (1.03) }= n\]
So: n = approx. 10
Aka the best domain would be (0,10)... maybe 11.

Answer 3

Part B:
What is the y-intercept?

\[f(n)=12(1.03)^n\]

Let n=0 & Solve

.... (0, f(0)) = y-intercept.

Answer 4

Part C:

Average rate of change formula:

\[\frac{ s(a)-s(b) }{ a-b }\]

So:
Find

\[\frac{ f(3)-f(10) }{ 3-10 }\]

Answer 5

@ItryMath Did i lose you lol

Answer 6

YOU ARE A MACHINE OMMMG

Answer 7

lol

Answer 8

math machine *

Answer 9

Lol thank you :D I am just happy to be your helper (:

Answer 10

what is In

Answer 11

@sunnnystrong

Answer 12

@ItryMath
Natural log. To solve for variables in the exponent you have to take the natural log (:

Answer 13

ive never heard of it

Answer 14

my teacher never mentioned it

Answer 15

Oh well natural logs are fun :D

Answer 16

do i have to include th In?

Answer 17

Hmmm... well that is one way to solve this problem.
If you aren't familiar with how to do natural logs I can show you briefly how to do it? :D

Answer 18

http://www.purplemath.com/modules/logs3.htm or here is a link with more information.

Basically: it is the inverse of an exponential function which allows me to solve for variables in the exponents

Answer 19

how do i answer part C? @sunnnystrong

Answer 20

Okay so:

Recall that ^^^ Up there we already talked about average rate of change -->

Solving for
\[\frac{ f(3)-f(10) }{ 3-10 }\]

When \[f(x)=12(1.03)^x\]

f(3)=approx. 13.112
f(10)= approx.16.1269

13.112-16.1269=-3.014
-3.014/-7= 0.4306 approx.

Answer 21

ooh

Answer 22

lmao thanks

Answer 23

Now: what does this mean?

Answer 24

nooo why would you ask me that :(

Answer 25

jk um let me find out xD

Answer 26

lol XD just think about it and let me know

Answer 27

it means the rate of change ...

Answer 28

@ItryMath ... Well yes.

But what does the slope of the function tell us -->
It tells us the change in height of the plant as time passes.

So the average rate of change between the 3rd & 10th day of 0.43 tells us that on avg. the plant grew 0.43 cm each day (:

Answer 29

thanks so much!!!im awful at math lol even though i love it xD its something i can really practice on and try mastering, even when its hard and you figure out how to do it , it feels great!!!! idk why i told you probably because you a math machine and obviously you didnt become on by not doing math lmao

Answer 30

@ItryMath oh thanks XD

well! to be honest with you the only way you can get good at math is by practicing everyday! everyone makes mistakes here and there though(: so we're all still learning

Answer 31

@mathmale do you see where she explained the In thing how did she get approx. 10?

Answer 32

Glad to respond, but ask that you be a lot more specific about what you want to learn from me. "That ln thing" is extremely important in math, so I'd suggest you look up "exponential and logarithmic functions" in your textbook or other learning material and study it. Yes, expo fns are the inverses of log functions, and vice versa.

Answer 33

can you explain me how she got approx. 10 though :)

Answer 34

exponential means non-constant rate of growth correct?

Answer 35

Logarithmic means constant rate of change

Answer 36

\[\frac{ \ln (16.13) - \ln (12) }{ \ln (1.03) }= n\]
1) evaluate ln 16.13. Use your calculator. Type in Ln(16.13) ENTER. You must know how to do this.

Answer 37

okay hold on

Answer 38

ln 16.13= 2.78, approx.
Now find ln 12 and ln 1.03.

Evaluate the numerator.
Divide your result by the denom.

Answer 39

i dont think i have Ln on my calculator ...

Answer 40

i have a scientific calculator

Answer 41

wait i do nvm

Answer 42

Does it have the function \[e^x\]

Answer 43

@mathmale MATHMALE!!!!!!!!!!!!!!!!!!

Answer 44

on one of its keys?

Answer 45

YOU ARE THE BEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 46

:)

Answer 47

this world needs more people like you !!!

Answer 48

Thank you. Even if I get up, go out to the kitchen and grab some peanuts while you wait for me?

Answer 49

sure!!!!! bring me some too

Answer 50

I'll mail them to you, postage due.

Answer 51

Okay thanks !

Answer 52

\[\frac{ \ln (16.13) - \ln (12) }{ \ln (1.03) }= n\]

ln 16.13=2.78 (approx).
ln 12=?
ln 1.03=?

Answer 53

10.00629

Answer 54

thats the answer :)

Answer 55

Isn't that pretty close to 10?
You were asking how your other helper got 10.

Answer 56

Now you've gotten 10 also.

Answer 57

Or close to it. ;)

Answer 58

yes

Answer 59

no i didnt know how to multiply that Ln stuff until now xD

Answer 60

@mathmale does the y-intercept here mean the rate of change of the trees growth over a certain period of time?

Answer 61

Actually, the y-intercept tells you how many trees you had at the very beginning (when t=0).

In this problem, "rate of change" signifies "number of trees present at a given time" divided by the elapsed time. For example:

25 trees - 14 trees 21 trees
----------------- = ---------
3 years - 2 years 1 year

which states that "the average growth rate in the number of trees is 21 trees per year" ... note that this is true ONLY for the period 2 years to 3 years.

If the period were 5 years to 7 years, then you'd get a different answer.

Rates of change vary, just as functions vary.