anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@Michele_Laino
Michele_Laino
  • Michele_Laino
please wait I have to answer to my phone
anonymous
  • anonymous
alright:)

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Michele_Laino
  • Michele_Laino
here I am!
anonymous
  • anonymous
yay! ok so I got part B and part C. all I need is A
Michele_Laino
  • Michele_Laino
is your function like below: \[\Large f\left( n \right) = 12 \cdot {1.03^n}\]
anonymous
  • anonymous
yes, just with parenthesis but that don't realy matter that much.
Michele_Laino
  • Michele_Laino
then we have to search for the value for n0, approximated by excess, such that: \[\Large 16.13 = 12 \cdot {1.03^{{n_0}}}\]
anonymous
  • anonymous
ok so we will put what on both sides? ik that we have to do that.
Michele_Laino
  • Michele_Laino
hint: using decimal logarithms we can write: \[\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = ...?\]
anonymous
  • anonymous
16.3/12=1.35/1.03=1.31 correct?
Michele_Laino
  • Michele_Laino
not exactly since we have to compute this: \[\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = \frac{{\log \left( {1.35} \right)}}{{\log \left( {1.03} \right)}} = ...?\]
anonymous
  • anonymous
im still getting 1.31 from 1.35/1.03...
Michele_Laino
  • Michele_Laino
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
Michele_Laino
  • Michele_Laino
compute*
anonymous
  • anonymous
ok so im trying to find the ratio between 1.31 and 1.03?
Michele_Laino
  • Michele_Laino
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: \[\Large \left\{ {0,1,2,3,4,5,6,7,8,9,10,11} \right\}\]
anonymous
  • anonymous
@peachpi
anonymous
  • anonymous
@Michele_Laino is that all?
anonymous
  • anonymous
@peachpi what would be the domain? it don't seem exactly like the one I did with you.
anonymous
  • anonymous
The domain would be the set of numbers @Michele_Laino entered, assuming they don't want to include partial day.
anonymous
  • anonymous
so the domain is just those numbers? so that's what I would put.?
anonymous
  • anonymous
yes. you could also say [0, 11] if you prefer a continuous function
anonymous
  • anonymous
ok, well thanks. can I tag you in some other questions @peachpi ?
anonymous
  • anonymous
sure, but I come and go
anonymous
  • anonymous
ok.

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