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

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

Answer 1

@SolomonZelman

Answer 2

Think of a visual graph. Where does the y-intercept happen on this graph?

Answer 3

on the y axis

Answer 4

what is x equal to for any point on the y axis?

Answer 5

0

Answer 6

so in this case, they're using n instead of x (doesn't matter really)

Answer 7

so the y intercept happens when n = 0

Answer 8

plug in n = 0 into the function and tell me what you get

Answer 9

y=12

Answer 10

so the y-intercept is the point (0,12) meaning that on day 0, ie the starting day, the height of the plant is 12 cm

Answer 11

basically the starting height is 12 cm

Answer 12

okay thank you!!

Answer 13

you're welcome

Answer 14

The y intercept of the graph of the function f(n) represents that when n=0 the height is 12. So when there are 0 days the height of the plant will be 12 cm. is that okay?

Answer 15

The last sentence is a bit odd. I'd say, on day 0, the height is 12 cm.

Answer 16

But you have it down for the most part.

Answer 17

oh okay, can you help me with one more corresponding question?

Answer 18

sure

Answer 19

What is the average rate of change of the function f(n) from n = 3 to n = 10 and what does it represent?

Answer 20

The average rate of change is simply the slope of the line through the two points where n = 3 and n = 10

Answer 21

So you first need to find f(3) and f(10)

Answer 22

kay, one moment please

Answer 23

f(3)= 13.11 and f(10)= 16.13

Answer 24

Those are basically what I'm getting as well (just with longer decimals)

Answer 25

f(3) = 13.11 means you have the point (3, 13.11)

f(10) = 16.13 means you have the point (10,16.13)

Answer 26

You have these two points (3, 13.11) & (10,16.13)

Finding the slope through them is the same as finding the avg rate of change from n = 3 to n = 10

Answer 27

okay so i'll do 16.13-13.11/10-3?

Answer 28

correct

Answer 29

I get 0.431428714

Answer 30

I'm getting the same if you compute (16.13-13.11)/(10-3)

It turns out that a more accurate answer is 0.43061036458991

So you're correct to 2 decimal places

Answer 31

To get 0.43061036458991, I computed (16.1269965521294-13.112724)/(10-3)

Answer 32

yes that is what I got can you help me with another question if you want?

Answer 33

go for it

Answer 34

The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.

The price f(x), in dollars, of product A after x years is represented by the function below.

f(x) = 0.69(1.03)^x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.

Answer 35

Ok post any thoughts or how far you got

Answer 36

okay I plugged in numbers 1,2,3,4 for the exponent

Answer 37

and what did you notice?

Answer 38

then gathered the info of f(1)= 0.7107, f(2)=0.732021, f(3)= 0.75398163 , f(4)=0.7766010789

Answer 39

that's where I stopped

Answer 40

So is the price of product A increasing over time? or decreasing over time?

Answer 41

increasing but it asks for percentages

Answer 42

hint: try to write 1.03 in the form 1+r

Answer 43

r will be the rate of increase

Answer 44

i don't get it

Answer 45

what do i multiply or divide?

Answer 46

we can break up 1.03 into 1+0.03

that matches the form 1+r where r = 0.03

Answer 47

So product A is increasing in price 3% each year (ie inflation for this product is 3%)

Answer 48

you divided to find the percentage?

Answer 49

no I just broke up 1.03 into 1+0.03

Then you take 0.03 and multiply it by 100 to get 0.03*100 = 3%

Answer 50

okay, how will i find the percentage for part B?

Answer 51

find the difference in price from year 1 to year 2

Answer 52

then divide that by the price in year 1

finally, multiply that result by 100 to get a percentage

Answer 53

so it will be10,201-10,100= 101

Answer 54

then 101/10100= 0.01

Answer 55

so far, so good

Answer 56

0.01*100= 1%

Answer 57

So the price increased by 1% from year 1 to year 2 (for product B)

Answer 58

What's the percentage increase from year 2 to year 3?

Answer 59

okay i get 1%

Answer 60

how about from year 3 to year 4?

Answer 61

1%

Answer 62

well i got 0.999999 but i rounded it

Answer 63

so basically the inflation is 1% throughout each year

Answer 64

yes thank you

Answer 65

np