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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 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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  1. anonymous
    • one year ago
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    @Michele_Laino

  2. Michele_Laino
    • one year ago
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    please wait I have to answer to my phone

  3. anonymous
    • one year ago
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    alright:)

  4. Michele_Laino
    • one year ago
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    here I am!

  5. anonymous
    • one year ago
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    yay! ok so I got part B and part C. all I need is A

  6. Michele_Laino
    • one year ago
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    is your function like below: \[\Large f\left( n \right) = 12 \cdot {1.03^n}\]

  7. anonymous
    • one year ago
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    yes, just with parenthesis but that don't realy matter that much.

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

  9. anonymous
    • one year ago
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    ok so we will put what on both sides? ik that we have to do that.

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

  11. anonymous
    • one year ago
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    16.3/12=1.35/1.03=1.31 correct?

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

  13. anonymous
    • one year ago
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    im still getting 1.31 from 1.35/1.03...

  14. Michele_Laino
    • one year ago
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    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

  15. Michele_Laino
    • one year ago
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    compute*

  16. anonymous
    • one year ago
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    ok so im trying to find the ratio between 1.31 and 1.03?

  17. Michele_Laino
    • one year ago
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    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: \[\Large \left\{ {0,1,2,3,4,5,6,7,8,9,10,11} \right\}\]

  18. anonymous
    • one year ago
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    @peachpi

  19. anonymous
    • one year ago
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    @Michele_Laino is that all?

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

  21. anonymous
    • one year ago
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    The domain would be the set of numbers @Michele_Laino entered, assuming they don't want to include partial day.

  22. anonymous
    • one year ago
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    so the domain is just those numbers? so that's what I would put.?

  23. anonymous
    • one year ago
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    yes. you could also say [0, 11] if you prefer a continuous function

  24. anonymous
    • one year ago
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    ok, well thanks. can I tag you in some other questions @peachpi ?

  25. anonymous
    • one year ago
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    sure, but I come and go

  26. anonymous
    • one year ago
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    ok.

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