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).

- anonymous

- chestercat

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- 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

- ganeshie8

For 5% growth it should be
f(x)=100*(\(\color{red}{1}\).05)^5

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## More answers

- 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

Other than that, your work looks fine!
good job!

- anonymous

Oh because we don't know how many years

- anonymous

Alright how would I create the domain and range?

- 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

Domain is all the possible numbers that you can feed into that function box
what numbers make sense for years ?

- anonymous

anything above 1

- 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

range is all the possible numbers that the function box spits out

- ganeshie8

see if you can make a good guess about the range

- anonymous

\[0\le x\]

- anonymous

I know that's wrong

- ganeshie8

whats the starting population of frogs ?

- anonymous

100

- anonymous

\[100\le x\]

- ganeshie8

since the populaiton in increasing, can the funciton box ever spit out anything less than 100 ?

- anonymous

No it cannot

- ganeshie8

Good! range is \(\color{red}{y} \ge 100\)

- 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

|dw:1437016788202:dw|

- anonymous

Oh I get it now
I just don't get which sign to put

- ganeshie8

what do you mean "which sign to put"

- anonymous

\[\le \ge \]

- anonymous

Those ^

- ganeshie8

\(\gt\) is read as "greater than"

- ganeshie8

To say, "my score is greater than 90", you may say :
my score \(\gt \) 90

- 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

To say, "y is greater than 100", you may say :
y \(\gt \) 100

- anonymous

I think I get it now and I think I got it from here with the graph. Thank you!

- ganeshie8

good!

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