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GalacticPlunder
 one year ago
Iris has been studying an invasive population of snails. This particular snail has no local predators, so the population grows wildly. She has observed that the population follows an exponential rate of growth for fifteen years.
GalacticPlunder
 one year ago
Iris has been studying an invasive population of snails. This particular snail has no local predators, so the population grows wildly. She has observed that the population follows an exponential rate of growth for fifteen years.

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GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.01. 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.

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.02. 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.

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.03. 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 yintercept would be, and if the function is increasing or decreasing.

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.04. 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.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1EZ! you just need to make an exponential function up  any exponential function you like. An exponential function (abstractly) is in a form of \(\large\color{black}{ \displaystyle y=a(b)^x }\) I will assume you know: \(\large\color{black}{ \displaystyle {\rm C}^0=1 }\) (for any nonzero number C)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\LARGE\color{black}{ \displaystyle \color{darkgoldenrod}{y}=\color{red}{a}(\color{blue}{b})^{\color{green}{x}} }\) \(\normalsize \color{black}{ \displaystyle \color{darkgoldenrod}{\rm Number~of~snalis}=\color{red}{\rm Initial~population}\cdot (\color{blue}{\rm growth~rate})^{\color{green}{\large ~\rm \text{#}~of~years }} }\)

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0So I just input random numbers?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, but a must be positive, and b>1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So that you don't end up getting a negative population.... and I would advise to choose Natural numbers for a and b.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1natural numbers are: 1 , 2, 3, 4, 5, 6, 7, etc....

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0I'm still kind of stuck.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1try to put random values for a and b (once)

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0Would y=10, a=5, b=2, x=2 work?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you don't need to plug in anything for x and y.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So you created a function: \(\large\color{black}{ \displaystyle y=5(2)^x }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now lets explain to Iris (:O) what is what....

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0Ok... so how would I explain it?

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0Y= Number of snails a=Initial population⋅ b=growth rate x=number of years ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Lets do that together. You need to explain what and why is the principal (initial) population of snails & what and why is the rate of growth of the population.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, will you agree that the initial population is at year zero, or in other words when x=0?

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0Ok. So that would mean a = 0?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle y=5(2)^x }\) Initially (at year zero  i.e. at x=0) \(\large\color{black}{ \displaystyle y=5(2)^0 }\) \(\large\color{black}{ \displaystyle y=5(1) }\) \(\large\color{black}{ \displaystyle y=5 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1See why the initial/principal population (when x=0) is (equivalent to) 5 (snails) ?

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0So there was no increase?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1There is going to be an increase as years pass by, BUT the population didn't increase right away when started.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1This that we are discussing right now is just the principal population  or from what number of snails did we start.

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok. I get it now. So what would be the starting number? And how would I explain my function?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I will be gone. tag someone else. (I am constructing my basement and bath)

GalacticPlunder
 one year ago
Best ResponseYou've already chosen the best response.0Ok thanks for helping.
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