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anonymous
 one year ago
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 yintercept 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)
anonymous
 one year ago
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 yintercept 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)

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1please wait I have to answer to my phone

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yay! ok so I got part B and part C. all I need is A

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1is your function like below: \[\Large f\left( n \right) = 12 \cdot {1.03^n}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, just with parenthesis but that don't realy matter that much.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then we have to search for the value for n0, approximated by excess, such that: \[\Large 16.13 = 12 \cdot {1.03^{{n_0}}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so we will put what on both sides? ik that we have to do that.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: using decimal logarithms we can write: \[\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = ...?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.016.3/12=1.35/1.03=1.31 correct?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1not 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
 one year ago
Best ResponseYou've already chosen the best response.0im still getting 1.31 from 1.35/1.03...

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1please we have to comute the ratio between the logarithm of 1.31 and the logarithm of 1.03, being both logarithms are decimal logarithms

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so im trying to find the ratio between 1.31 and 1.03?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: 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
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino is that all?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@peachpi what would be the domain? it don't seem exactly like the one I did with you.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The domain would be the set of numbers @Michele_Laino entered, assuming they don't want to include partial day.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the domain is just those numbers? so that's what I would put.?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. you could also say [0, 11] if you prefer a continuous function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, well thanks. can I tag you in some other questions @peachpi ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sure, but I come and go
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