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#1 2021-04-17 08:33:56

mathland
Member
Registered: 2021-03-25
Posts: 444

Population of Animals

A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2014 was estimated to be 50 animals. If P represents the population n years after 2014, write an equation that represents the class model of the population over time?

Let me see.

A general formula that I think applies here is y = ab^x.

Let a = 50

Let b = double or 2

We get P = 50(2)^12n. Here 12 represents the months of a year.

A friend told me that the correct answer is P = 50(2)^(n/12).

Is my friend right? If so, why is my set up wrong?

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#2 2021-04-17 11:24:16

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Population of Animals

A general formula that I think applies here is y = ab^x.

Let a = 50

Let b = double or 2

We get P = 50(2)^12n. Here 12 represents the months of a year.

A friend told me that the correct answer is P = 50(2)^(n/12).

Is my friend right? If so, why is my set up wrong?

Try plugging in a couple of values into your equation after developing it - it'll help a ton, especially when it comes to these equations modelling real life.

Since the population of animals at Central High School doubles every 12 years, the period is 12. So when n = 12, we should expect the population to double. If we plug n=12 years into your equation, we see the population skyrockets to an eyewatering 1.11*10^45. Clearly not a doubling in a year.

As we want the population of animals to double in this exponential model, we want P=100 when n=12, so let's solve a simple mathematical equation to determine the exponent's power.

Let k be a real-valued number.
population = base*(how much the population increases every period number of years)^(n*k)
100 = 50*2^(12*k) (divide by 50)
2 = 2^(12*k)

Obviously, to equalize both sides, k must be 1/12. Hence, your friend is right - the exponential function modelling the population of animals is indeed 50*(2)^(n/12).

Last edited by Mathegocart (2021-04-17 11:27:19)


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#3 2021-04-18 06:28:57

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Population of Animals

Mathegocart wrote:

A general formula that I think applies here is y = ab^x.

Let a = 50

Let b = double or 2

We get P = 50(2)^12n. Here 12 represents the months of a year.

A friend told me that the correct answer is P = 50(2)^(n/12).

Is my friend right? If so, why is my set up wrong?

Try plugging in a couple of values into your equation after developing it - it'll help a ton, especially when it comes to these equations modelling real life.

Since the population of animals at Central High School doubles every 12 years, the period is 12. So when n = 12, we should expect the population to double. If we plug n=12 years into your equation, we see the population skyrockets to an eyewatering 1.11*10^45. Clearly not a doubling in a year.

As we want the population of animals to double in this exponential model, we want P=100 when n=12, so let's solve a simple mathematical equation to determine the exponent's power.

Let k be a real-valued number.
population = base*(how much the population increases every period number of years)^(n*k)
100 = 50*2^(12*k) (divide by 50)
2 = 2^(12*k)

Obviously, to equalize both sides, k must be 1/12. Hence, your friend is right - the exponential function modelling the population of animals is indeed 50*(2)^(n/12).

A great,  detailed reply. Please, look for my questions from now on. I know that Bob is always on the look out for my threads. Maybe you guys can share in terms of reply. If I don't show my work, it simply means that I haven't the slightest idea how to begin to post an answer. Otherwise, I show work or effort. Is there a way to upload pictures on this site? I am thinking geometry,, trigonometry and calculus questions involving a geometric interpretation. You say?

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#4 2021-04-19 07:26:46

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Population of Animals

A great,  detailed reply. Please, look for my questions from now on. I know that Bob is always on the look out for my threads. Maybe you guys can share in terms of reply. If I don't show my work, it simply means that I haven't the slightest idea how to begin to post an answer. Otherwise, I show work or effort. Is there a way to upload pictures on this site? I am thinking geometry,, trigonometry and calculus questions involving a geometric interpretation. You say?

I always attempt to do a general review of the forum twice a day(when I can, of course.).

Try the [img]IMAGEURL[/img] tag. For example, this is an url of a bunch of blue balloons: https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg .Place this url where the IMAGEURL is.

As for a geometric approach to tackling down problems, why not? Mathematics is beautiful in its multifactorial ways to represent the same problem, concept, or idea.

78e149af9501adae51dae96faa2307dd.jpg

Last edited by Mathegocart (2021-04-19 07:27:47)


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#5 2021-04-19 09:21:03

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Population of Animals

Mathegocart wrote:

A great,  detailed reply. Please, look for my questions from now on. I know that Bob is always on the look out for my threads. Maybe you guys can share in terms of reply. If I don't show my work, it simply means that I haven't the slightest idea how to begin to post an answer. Otherwise, I show work or effort. Is there a way to upload pictures on this site? I am thinking geometry,, trigonometry and calculus questions involving a geometric interpretation. You say?

I always attempt to do a general review of the forum twice a day(when I can, of course.).

Try the [img]IMAGEURL[/img] tag. For example, this is an url of a bunch of blue balloons: https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg .Place this url where the IMAGEURL is.

As for a geometric approach to tackling down problems, why not? Mathematics is beautiful in its multifactorial ways to represent the same problem, concept, or idea.

https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg


Going back to the picture, can you provide the steps?

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#6 2021-04-19 13:34:40

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Population of Animals

mathland wrote:
Mathegocart wrote:

A great,  detailed reply. Please, look for my questions from now on. I know that Bob is always on the look out for my threads. Maybe you guys can share in terms of reply. If I don't show my work, it simply means that I haven't the slightest idea how to begin to post an answer. Otherwise, I show work or effort. Is there a way to upload pictures on this site? I am thinking geometry,, trigonometry and calculus questions involving a geometric interpretation. You say?

I always attempt to do a general review of the forum twice a day(when I can, of course.).

Try the [img]IMAGEURL[/img] tag. For example, this is an url of a bunch of blue balloons: https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg .Place this url where the IMAGEURL is.

As for a geometric approach to tackling down problems, why not? Mathematics is beautiful in its multifactorial ways to represent the same problem, concept, or idea.

https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg


Going back to the picture, can you provide the steps?

Sure. To upload a personal image of yours onto this forum,
1. Upload the image to an image hoster such as postimage. Others have suggested imgur in the past, but it has now been infested with commercialism and other such idiocies of the Internet. Hence why I recommend postimage.

2.  On the page after you upload your image, you will be presented with a myriad of links. Copy and paste the Direct Link into an  tag, i.e [img]DIRECT LINK GOES HERE[/img].

Last edited by Mathegocart (2021-04-19 13:35:27)


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Offline

#7 2021-04-19 15:21:36

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Population of Animals

Mathegocart wrote:
mathland wrote:
Mathegocart wrote:

I always attempt to do a general review of the forum twice a day(when I can, of course.).

Try the [img]IMAGEURL[/img] tag. For example, this is an url of a bunch of blue balloons: https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg .Place this url where the IMAGEURL is.

As for a geometric approach to tackling down problems, why not? Mathematics is beautiful in its multifactorial ways to represent the same problem, concept, or idea.

https://i.pinimg.com/736x/78/e1/49/78e149af9501adae51dae96faa2307dd.jpg


Going back to the picture, can you provide the steps?

Sure. To upload a personal image of yours onto this forum,
1. Upload the image to an image hoster such as postimage. Others have suggested imgur in the past, but it has now been infested with commercialism and other such idiocies of the Internet. Hence why I recommend postimage.

2.  On the page after you upload your image, you will be presented with a myriad of links. Copy and paste the Direct Link into an  tag, i.e [img]DIRECT LINK GOES HERE[/img].

I have to join postimage first, right?

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#8 2021-04-20 03:20:13

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Population of Animals

mathland wrote:
Mathegocart wrote:
mathland wrote:

Going back to the picture, can you provide the steps?

Sure. To upload a personal image of yours onto this forum,
1. Upload the image to an image hoster such as postimage. Others have suggested imgur in the past, but it has now been infested with commercialism and other such idiocies of the Internet. Hence why I recommend postimage.

2.  On the page after you upload your image, you will be presented with a myriad of links. Copy and paste the Direct Link into an  tag, i.e [img]DIRECT LINK GOES HERE[/img].

I have to join postimage first, right?

You may if you wish, but it's not necessary for uploading images.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Offline

#9 2021-04-20 10:57:58

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Population of Animals

Mathegocart wrote:
mathland wrote:
Mathegocart wrote:

Sure. To upload a personal image of yours onto this forum,
1. Upload the image to an image hoster such as postimage. Others have suggested imgur in the past, but it has now been infested with commercialism and other such idiocies of the Internet. Hence why I recommend postimage.

2.  On the page after you upload your image, you will be presented with a myriad of links. Copy and paste the Direct Link into an  tag, i.e [img]DIRECT LINK GOES HERE[/img].

I have to join postimage first, right?

You may if you wish, but it's not necessary for uploading images.

There are questions that involve geometric figures. So, it is important for me to upload pictures to increase a better understanding of the problem, especially when I get to applications of the derivative. Related rates comes to mind right away.

Last edited by mathland (2021-04-20 10:58:34)

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