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) = 10(1.02)n

Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)

Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)

Answer 1

@Hero

Answer 2

@satellite73 @

Answer 3

Plz help!

Answer 4

@ParthKohli

Answer 5

A. 0 thru 5 (integers) ... (look at part C)
B. the starting height of the plant
C. f(1) = 10.02 .... f(5) = 11.041
m(ave) = (11.041 - 10.02) / (5 - 1) = 0.255 cm/day
this represents the average change of height each day for this time.

Answer 6

Can I get the explanations please?

Answer 7

For the firat part you need toknow what reasonable values of n will be plotted on the chart

you know that at the end of the trial (i.e after n days) the height is

11.04cm

but also that this is 10(1.02)^n

so use logs to find n

Answer 8

ok, im confused

Answer 9

the trial lasts n days

after n days the height is 11.04cm

but height = 10(1.02)^n

so 11.04 = 10 (1.02)^n

use the propoerties of logs and exponents to find n

Answer 10

oh ok, so n = 5?

Answer 11

did oyu use the properties of logs and exponents to get that?

show yourwork?

Answer 12

Ok so,

11.04 = 10(1.02)^n
10(1.02)^n = 11.04
10(1.02)^n/10 = 11.04/10
1.02^n = 1.104
log(1.02)^n = log(1.104)
n*(log(1.02)) = log(1.104)
n = log(1.104)/(log(1.02)
n = 4.99 (round to 5)

Answer 13

ok....

Answer 14

OK well done

now second part

the y intercept is when n=0

what does that value mean?

Answer 15

It represents the starting population. right?

Answer 16

not the population - since we are measuring height (but I think you've got the right idea)
(this exponential function of DOES represent populations! :-)

Answer 17

Ok so that's part b?

Answer 18

so wht IS the staring height (it doesnt ask oyu that - but you maybe would lik eot know?)

Answer 19

Um... .21 cm?

Answer 20

no -
put n= 0 into the equation for height....

Answer 21

Ok... But the answer cant be true...

Answer 22

You should also get into th ehabit of doing a 'sanity check' on oyur answers

If it is 11cm after 5 days it cannot be 21cm at start.

And the answer CAN be true

what is 1.02^0??

Answer 23

1!

Answer 24

so 10* (1.02)^0 is??

Answer 25

10

Answer 26

Im srry, I thought you meant to do the whole equation with 11.04=10(1.02)^0

Answer 27

good

so it starts at 10cm

and grows to 11.04 in 5 days

the 3rd part says

find change of height over 4 days and divide by 4 days

so what does that give you?