Question

@inkyvoyd @mathmale @phi 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) = 8(1.05)n

Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm. What is a reasonable domain to plot the growth function?

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

Part C: What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent?

Answer 1

@inkyvoyd @mathmale @phi This is all I have so far and I really need help: :'(

Part A:
The plant is 11.26 cm tall at the end. How many days?
We use 8(1.05)^n=(height of plant)=11.26
To find ‘n’ divide by 8: 8(1.05)^n=11.26 〖1.05〗^n=1.4075

Answer 2

I don't know why there are question marks, but please ignore them

Answer 3

use logs to solve for n

\[ 1.05^n = 1.4075 \]
take the log of both sides
\[ \log(1.05^n) = \log(1.4075) \]
now use the useful property
\[ \log(a^b) =b \log(a) \]

Answer 4

How do I find the log?

Answer 5

you should get
n log(1.05) = log(1.4075)
divide both sides by log(1.05)
n= log(1.4075)/ log(1.05)

it's time to dust off your calculator

Answer 6

you can use either log (base 10) or ln (log base 3)
it does not matter which.

or you can type into google
log(1.4075)/ log(1.05)=

Answer 7

I got 7

Answer 8

that means a reasonable domain (of x values) is from 0 days up to 7 days

Answer 9

that was part A.
can you do part B?

Answer 10

If the x values are the days, then shouldn't the y values be the height in which it grew for part b?

Answer 11

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

y-intercept means the y value *on the y-axis* i.e. when x=0
so it's a specific point.

Answer 12

Part A:
Domain will be talking about the values of n.
Now when we solve for f(n) = 11.26 we get 7.005... so a reasonable range to plot the graph would be from n = 0 to 8

Part B:
The y-intercept is the point where n = 0. But n represents the number of days, i.e. time elapsed. So at n = 0 the point represents the initial reading.

Part C:
At n = 2, f(2) = 8*(1.05)^2 = 8.82
At n = 6, f(6) = 8*(1.05)^6 = 10.72
The average rate of change is (change in height)/(change in n)
The change in height is 10.72 - 8.82 = 1.9
The change in n is 6 - 2 = 4
So the average rate of change is 1.9/4 = 0.475
But what is the average rate of change? It is the average daily (because a single change in n corresponds to a day) growth of the plant (because f(n) represents height)

Enjoy :)

Answer 13

I am slightly lost @phi Apple_pi 's answer seems different from what you said it would be

Answer 14

what is confusing ?

Answer 15

You said that it would be a specific number. apple_pi said that n=0. I don't understand what apple_pi is saying.

Answer 16

And I definitely don't know if it is the same thing you are saying

Answer 17

the y-intercept is the y value when x = 0
or in this case, where they are using n instead of x, where n=0

Answer 18

The graph will look something like this

Answer 19

This is the y-intercept

Answer 20

Okay. So, when n=0, the y intercept is the height in which it has grown in 0 days?

Answer 21

they want you to know that the y-value when n=0 is (this is logic or common sense), the height of the plant at day 0

Answer 22

Yeah, or rather it hasn't grown because it hasn't had time to grow

Answer 23

I understand now. For C, how do I find the average rate of change?
I know it is ƒ(b) − ƒ(a) over b − a

Answer 24

f(b)-f(a) over b-a

Answer 25

But how do I figure out what is f(b) and what is f(a) ?

Answer 26

use the equation they gave you. apple did the work

Answer 27

Okay. Thank you!

Answer 28

but it's good practice to do it yourself

Answer 29

That is what I was trying to do

Answer 30

you need a calculator (or google)

Answer 31

I still am having difficulty finding f(a) or f(b). How do I know what is f(A) or f(b)

Answer 32

I would do the f(6) - f(2) divided by (6-2)

you could also do f(2) - f(6) divided by 2 - 6 (that works, but seems backwards)

Answer 33

and f(6) is short-hand for find the definition of f(n),
which is
f(n) = 8(1.05)^n

replace the "n" with a 6, like this

f(6) = 8(1.05)^6

and now use a calculator
8 times 1.05 ^ 6

Answer 34

I got 10.72

Answer 35

yes. one down, one to go
find f(2)

Answer 36

8.82

Answer 37

yes, now find the difference

Answer 38

1.9