anonymous
  • anonymous
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).
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
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?
anonymous
  • anonymous
ganeshie8
  • ganeshie8
For 5% growth it should be f(x)=100*(\(\color{red}{1}\).05)^5

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ganeshie8
  • ganeshie8
Also, replace 5 by x because the variable "x" represents the number of years : f(x)=100*(\(\color{red}{1}\).05)^\(\color{red}{x}\)
ganeshie8
  • ganeshie8
Other than that, your work looks fine! good job!
anonymous
  • anonymous
Oh because we don't know how many years
anonymous
  • anonymous
Alright how would I create the domain and range?
ganeshie8
  • ganeshie8
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|
ganeshie8
  • ganeshie8
Domain is all the possible numbers that you can feed into that function box what numbers make sense for years ?
anonymous
  • anonymous
anything above 1
ganeshie8
  • ganeshie8
they better be nonnegative because, for example, -2 years makes no sense in this context so the domain could be all nonnegative integers : \(x\ge 0\)
ganeshie8
  • ganeshie8
range is all the possible numbers that the function box spits out
ganeshie8
  • ganeshie8
see if you can make a good guess about the range
anonymous
  • anonymous
\[0\le x\]
anonymous
  • anonymous
I know that's wrong
ganeshie8
  • ganeshie8
whats the starting population of frogs ?
anonymous
  • anonymous
100
anonymous
  • anonymous
\[100\le x\]
ganeshie8
  • ganeshie8
since the populaiton in increasing, can the funciton box ever spit out anything less than 100 ?
anonymous
  • anonymous
No it cannot
ganeshie8
  • ganeshie8
Good! range is \(\color{red}{y} \ge 100\)
ganeshie8
  • ganeshie8
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)
ganeshie8
  • ganeshie8
|dw:1437016788202:dw|
anonymous
  • anonymous
Oh I get it now I just don't get which sign to put
ganeshie8
  • ganeshie8
what do you mean "which sign to put"
anonymous
  • anonymous
\[\le \ge \]
anonymous
  • anonymous
Those ^
ganeshie8
  • ganeshie8
\(\gt\) is read as "greater than"
ganeshie8
  • ganeshie8
To say, "my score is greater than 90", you may say : my score \(\gt \) 90
anonymous
  • anonymous
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
ganeshie8
  • ganeshie8
To say, "y is greater than 100", you may say : y \(\gt \) 100
anonymous
  • anonymous
I think I get it now and I think I got it from here with the graph. Thank you!
ganeshie8
  • ganeshie8
good!

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