Question

I WILL FAN AND GIVE MEDAL!
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

@phi Can i show you my work so far?

Answer 2

@SolomonZelman @aaronq

Answer 3

yes, what have you got so far?

Answer 4

For PART A plug in `11.26` for `f(n)` into ` f(n) = 8(1.05)ⁿ`

For PART B, y-intercept is when `n` =0 So plug in zero for n, to get the value of the y-intercept, but when n=0 it means that zero days have passed, in other words the initial height.


────────────────────────
1) Click and hold ALT

2) click the number code `2 5 2`
(using the numbers that are on the right of the keyboard,
not the ones below F1, F2, F3, etc., )

3) release the ALT

it should show ⁿ
────────────────────────

Answer 5

You can solve for C yourself

Answer 6

if you learned about average rate bf

Answer 7

11.26=8*(1.05)n 11.26=8.40n 11.26/8.40=n

Answer 8

@jadee27p
be careful. I am sure the equation is
\[ f(n) = 8 \cdot (1.05)^n \]

Answer 9

the "n" is an exponent. in other words, it is *not* 8*1.05*n

Answer 10

what did i do wrong?

Answer 11

f(n) at the end of the study is 11.26, so you say
\[ f(n) = 8 \cdot (1.05)^n \\ 11.26= 8 \cdot (1.05)^n \]
you can divide both sides by 8 to get
\[ \frac{11.26}{8}= 1.05^n \]
to get at the "n", you have to take the log of both sides

Answer 12

i just finished this

Answer 13

so i divide

Answer 14

what do you get ?

Answer 15

10.72

Answer 16

you did 11.26/1.05 but that is a different problem

so far you have
\[ \frac{11.26}{8}= 1.05^n \]
you can divide 8 into 11.26

Answer 17

.71

Answer 18

11.26/8 = ?

Answer 19

no that's 1.40

Answer 20

but i'm kinda lost right now.

Answer 21

Let's start at the beginning.

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?

the domain are the n values we should use. "n" is the number of days the plants were growing. n=0 is a good place to start.
we need to find the last day.

we know the plant is 11.26 cm tall at the end. How many days was that?

we use the formula that says
\[ 8 (1.05)^n= \text{height of plant} = 11.26 \]
we want to find n.

Answer 22

to find n we first divide both sides by 8
\[ 8(1.05)^n = 11.26 \\ 1.05^n= 1.4075 \]

do you follow this part ?

Answer 23

yes

Answer 24

the next step is trickier, because we use log
the rule for log is this:
\[ \log(a^b) = b \log(a) \]

with your equation , we "take the log" of both sides (we do the same thing to both sides, so it stays equal)

\[ \log(1.05^n) = \log(1.4075) \]
using the "rule" we can take the "n" out of the log, and write it
\[ n \log(1.05) = \log(1.4075) \]

Answer 25

log(1.05) is a number. If you use a calculator you can find it.
also, log(1.4075) is a different number.
you can find n because your equation tells you
n = log(1.4075)/log(1.05)

Answer 26

what is log?