anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
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
anonymous
  • anonymous
can you help me with the other parts too please?
anonymous
  • anonymous
what are they?
anonymous
  • anonymous
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.
anonymous
  • anonymous
You can use this rule \[(x^m)^n=x^{mn}\] So \[200(1.03)^{2x}=200(1.03^2)^x\]
anonymous
  • anonymous
then do 1.03² to find the growth rate for this one
anonymous
  • anonymous
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.
anonymous
  • anonymous
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)
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
you just saved my life! and can you make the 3d one a little more clear im struggling to solve the whole thing
anonymous
  • anonymous
which one?
anonymous
  • anonymous
200(1.03)^2x=200(1.032)^x
anonymous
  • anonymous
you have to do 1.03^2 to get the number in parentheses Then subtract 1 to get the growth rate as a decimal
anonymous
  • anonymous
so would it be f(x) = 200(1.0609)^x
anonymous
  • anonymous
yes
anonymous
  • anonymous
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?
anonymous
  • anonymous
to graph it..
anonymous
  • anonymous
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.
anonymous
  • anonymous
thank youuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
anonymous
  • anonymous
you're welcome

Looking for something else?

Not the answer you are looking for? Search for more explanations.