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anonymous

  • one year ago

Can someone take me through this problem? -Create an exponential growth function, f(x), to model a population of frogs that is growing every year. Identify the principal amount, the growth rate, and the appropriate domain and range for your function. Explain how these key features would affect the graph of f(x).

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  1. anonymous
    • one year ago
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    I came up with this function: f(x)=100*(0.05)^5 100 = the initial frog population 0.05 = that they grow 5% per year ^5 = 5 years Did I do this correctly?

  2. anonymous
    • one year ago
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    @ganeshie8

  3. ganeshie8
    • one year ago
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    For 5% growth it should be f(x)=100*(\(\color{red}{1}\).05)^5

  4. ganeshie8
    • one year ago
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    Also, replace 5 by x because the variable "x" represents the number of years : f(x)=100*(\(\color{red}{1}\).05)^\(\color{red}{x}\)

  5. ganeshie8
    • one year ago
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    Other than that, your work looks fine! good job!

  6. anonymous
    • one year ago
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    Oh because we don't know how many years

  7. anonymous
    • one year ago
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    Alright how would I create the domain and range?

  8. ganeshie8
    • one year ago
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    Kindof, it is because we can think of the function "f(x)" as a formula to which you feed in the number of years "x", and it spits out the population of frogs in that year. |dw:1437016213365:dw|

  9. ganeshie8
    • one year ago
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    Domain is all the possible numbers that you can feed into that function box what numbers make sense for years ?

  10. anonymous
    • one year ago
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    anything above 1

  11. ganeshie8
    • one year ago
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    they better be nonnegative because, for example, -2 years makes no sense in this context so the domain could be all nonnegative integers : \(x\ge 0\)

  12. ganeshie8
    • one year ago
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    range is all the possible numbers that the function box spits out

  13. ganeshie8
    • one year ago
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    see if you can make a good guess about the range

  14. anonymous
    • one year ago
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    \[0\le x\]

  15. anonymous
    • one year ago
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    I know that's wrong

  16. ganeshie8
    • one year ago
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    whats the starting population of frogs ?

  17. anonymous
    • one year ago
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    100

  18. anonymous
    • one year ago
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    \[100\le x\]

  19. ganeshie8
    • one year ago
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    since the populaiton in increasing, can the funciton box ever spit out anything less than 100 ?

  20. anonymous
    • one year ago
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    No it cannot

  21. ganeshie8
    • one year ago
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    Good! range is \(\color{red}{y} \ge 100\)

  22. ganeshie8
    • one year ago
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    Notice, the general convention is to use \(x\) for independent variable (what goes into the funciton), and \(y\) for dependent variable (what comes out of the function box)

  23. ganeshie8
    • one year ago
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    |dw:1437016788202:dw|

  24. anonymous
    • one year ago
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    Oh I get it now I just don't get which sign to put

  25. ganeshie8
    • one year ago
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    what do you mean "which sign to put"

  26. anonymous
    • one year ago
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    \[\le \ge \]

  27. anonymous
    • one year ago
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    Those ^

  28. ganeshie8
    • one year ago
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    \(\gt\) is read as "greater than"

  29. ganeshie8
    • one year ago
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    To say, "my score is greater than 90", you may say : my score \(\gt \) 90

  30. anonymous
    • one year ago
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    Right I get that. It's just that when it comes to writing the domain and the range I don't know which one to apply

  31. ganeshie8
    • one year ago
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    To say, "y is greater than 100", you may say : y \(\gt \) 100

  32. anonymous
    • one year ago
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    I think I get it now and I think I got it from here with the graph. Thank you!

  33. ganeshie8
    • one year ago
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    good!

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