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anonymous

  • one year ago

Create your own exponential function, f(x), which models the snail population. You will need to identify the principal population of the snails and the rate of growth each year. Explain to Iris how your function shows the principal population and the rate of growth, in complete sentences.

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  1. anonymous
    • one year ago
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    f(x) = principal population (1 + growth rate as decimal)^x Pick a number for the principal population (aka initial amount) and pick a number for the growth rate

  2. anonymous
    • one year ago
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    i got this but im not sure if im right: f(x) = 2(5)^x , because i chose 2 to start off with, and the number of growth rate is 5...

  3. anonymous
    • one year ago
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    or would i have to do it like this f(x) = 2(b)^5 ?

  4. anonymous
    • one year ago
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    ok that's great. So you started off with 2 snails and your growth rate is actually 400%. (5 = 1 + 4. The one is for the original amount, and the 4 is for the growth rate. 4 is the decimal form of 400%) f(x) = 2(5)^x is correct

  5. anonymous
    • one year ago
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    can you help me with the other parts too please?

  6. anonymous
    • one year ago
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    what are they?

  7. anonymous
    • one year ago
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    A local snail population grows according to the function g(x) = 200(1.03)2x. Demonstrate the steps to convert g(x) into an equivalent function with only x as the exponent. Then, explain to Iris how the key features of this local snail population compares to the key features of the invasive population.

  8. anonymous
    • one year ago
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    You can use this rule \[(x^m)^n=x^{mn}\] So \[200(1.03)^{2x}=200(1.03^2)^x\]

  9. anonymous
    • one year ago
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    then do 1.03² to find the growth rate for this one

  10. anonymous
    • one year ago
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    Iris wants to graph the invasive snail population to show the city council. Justify what the appropriate domain and range would be for the function f(x), what the y-intercept would be, and if the function is increasing or decreasing.

  11. anonymous
    • one year ago
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    y is the amount of snails and I assume x is time, so they both have to be greater than 0, and since the population is growing the function must be increasing. The y-intercept will be the principal amount (population when x = 0)

  12. anonymous
    • one year ago
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    last one, In five years, a garden festival plans on using the park where Iris has been studying the invasive snails. Explain to the garden festival committee how to find the average rate of change for the snail population between years 2 and 5. Describe what this average rate of change represents.

  13. anonymous
    • one year ago
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    average rate of change is basically the slope between two point on the function. This is the formula between 2 and 5. \[aroc=\frac{ f(5)-f(2) }{ 5-2}\] It would give the change in population over the 3 years.

  14. anonymous
    • one year ago
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    you just saved my life! and can you make the 3d one a little more clear im struggling to solve the whole thing

  15. anonymous
    • one year ago
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    which one?

  16. anonymous
    • one year ago
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    200(1.03)^2x=200(1.032)^x

  17. anonymous
    • one year ago
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    you have to do 1.03^2 to get the number in parentheses Then subtract 1 to get the growth rate as a decimal

  18. anonymous
    • one year ago
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    so would it be f(x) = 200(1.0609)^x

  19. anonymous
    • one year ago
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    yes

  20. anonymous
    • one year ago
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    and for the third one since it is growth in this situation, as the number heightens higher than it originally was, The range is [200, infinity) if the domain is [0, infinity) right?

  21. anonymous
    • one year ago
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    to graph it..

  22. anonymous
    • one year ago
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    yes. The domain is [0, inf). I suppose there's nothing wrong with making the range start at 200. I'd make is [0, inf) as well because population could technically drop below 200. But I think that's a personal choice.

  23. anonymous
    • one year ago
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    thank youuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu

  24. anonymous
    • one year ago
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    you're welcome

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