Question

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?

Answer 1

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

Answer 2

i have no idea *shrugs*

Answer 3

is f(n) = 8 ( 1.05)^n

Answer 4

yes

Answer 5

does anyone understand it?

Answer 6

HI!

Answer 7

hello

Answer 8

\[f(n) = 8(1.05)^n \] right ?

Answer 9

yes

Answer 10

the y intercept is the height when n= 0 , or at time = zero

Answer 11

ok

Answer 12

thats part b though

Answer 13

lol the plant grows exponentially!! 5% a day

Answer 14

it starts at \(f(0)=8\) mm tall

Answer 15

5%? are you sure

Answer 16

pretty sure dear, yes

Answer 17

5% is part A but what about part b

Answer 18

i guess you are supposed to solve
\[8(1.05)^n=11.26\] oh my dear you are confused

Answer 19

i answered B and @perl answered B already

Answer 20

oh what was b i didnt see it

Answer 21

and the answer to A is not 5% i just said it grew at 5% a day is all

Answer 22

What is a reasonable domain to plot the growth function?

Answer 23

i dont need you to solve

Answer 24

i need that

Answer 25

@Hero

Answer 26

The domain are the set of inputs , here days.
The study begins at n=0, and ends at what day ?

Answer 27

it was n number of days? so i dont know really

Answer 28

the domain will be n between 0 and some number. We don't want n to be too big because that will imply that the plant grows very high due to exponential growth. And notice that in the study the plant only grew to 11.26 cm

Answer 29

yeah

Answer 30

i could divide right?

Answer 31

we can solve this equation:
8(1.05)^n=11.26
to give us a rough upper bound for n

Answer 32

ok

Answer 33

8 x 1.05^2 =n?

Answer 34

then divide 11.26 by the number?

Answer 35

not quite

Answer 36

oh

Answer 37

8(1.05)^n=11.26

first divide both sides by 8

(1.05)^n = 11.26/8

Answer 38

oh i was close :P

Answer 39

:)

Answer 40

so let me see if i understand this correctly ...

Answer 41

step 1: i divide 11.26 by 8
step 2:(1.05)^n
final step: i fail the exam :P just kidding

Answer 42

but you know what, lets keep it simple. the domain is just n >= 0

Answer 43

number of days n is zero or positive, but not negative. that should be enough for reasonable domain

Answer 44

oh i think i got it plus i just looked up the domain again for better clarification. thanks :}

Answer 45

but before i close this is it ok if i ask a different question and then i tag you in? @perl

Answer 46

ok

Answer 47

ok brb

Answer 48

yes

Answer 49

i opened a new one

Answer 50

it starts with belinda