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)

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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
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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please wait I have to answer to my phone
alright:)

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

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