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) = 12(1.03)n

Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 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 = 3 to n = 10, and what does it represent? (4 points)

Answer 1

@Michele_Laino

Answer 2

please wait I have to answer to my phone

Answer 3

alright:)

Answer 4

here I am!

Answer 5

yay! ok so I got part B and part C. all I need is A

Answer 6

is your function like below:
\[\Large f\left( n \right) = 12 \cdot {1.03^n}\]

Answer 7

yes, just with parenthesis but that don't realy matter that much.

Answer 8

then we have to search for the value for n0, approximated by excess, such that:
\[\Large 16.13 = 12 \cdot {1.03^{{n_0}}}\]

Answer 9

ok so we will put what on both sides? ik that we have to do that.

Answer 10

hint:
using decimal logarithms we can write:
\[\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = ...?\]

Answer 11

16.3/12=1.35/1.03=1.31 correct?

Answer 12

not exactly since we have to compute this:
\[\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = \frac{{\log \left( {1.35} \right)}}{{\log \left( {1.03} \right)}} = ...?\]

Answer 13

im still getting 1.31 from 1.35/1.03...

Answer 14

please we have to comute the ratio between the logarithm of 1.31 and the logarithm of 1.03, being both logarithms are decimal logarithms

Answer 15

compute*

Answer 16

ok so im trying to find the ratio between 1.31 and 1.03?

Answer 17

hint:
using windows calculator, for example, we get this:
\[\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} \cong 10\]
so, a reasonable domain, it is given by the subsequent set:
\[\Large \left\{ {0,1,2,3,4,5,6,7,8,9,10,11} \right\}\]

Answer 18

@peachpi

Answer 19

@Michele_Laino is that all?

Answer 20

@peachpi what would be the domain? it don't seem exactly like the one I did with you.

Answer 21

The domain would be the set of numbers @Michele_Laino entered, assuming they don't want to include partial day.

Answer 22

so the domain is just those numbers? so that's what I would put.?

Answer 23

yes. you could also say [0, 11] if you prefer a continuous function

Answer 24

ok, well thanks. can I tag you in some other questions @peachpi ?

Answer 25

sure, but I come and go

Answer 26

ok.