what is wrong here?

[allegansveritatem]

Here is problem:


Here is how I solved it:


Here is the solution in back of the book:


Now, how can this be? I mean, all you need to do is eyeball the formula and know that that x is going to be 12 to know that you are going to get a number larger than 360. So, what am I missing. I tried doing various things with the 6x^3/2 but no matter what I did I always got an answer that in no way conforms to that little 360.

 

[Dr.Peterson]

Here is problem:
View attachment 10784

Here is how I solved it:
View attachment 10785

Here is the solution in back of the book:
View attachment 10786

Now, how can this be? I mean, all you need to do is eyeball the formula and know that that x is going to be 12 to know that you are going to get a number larger than 360. So, what am I missing. I tried doing various things with the 6x^3/2 but no matter what I did I always got an answer that in no way conforms to that little 360.

You must be misreading the problem somehow. It doesn't say that x is the number of years elapsed, and P is the increase; rather, x is the number of years since 1980 for one specific year, and P is the population in that year. The answer does not involve x=12 at all. What you found is the population in 1992.

To find the increase from 1984 to 1986, you have to find the population in each year, and then subtract. What is x for each year? What is P for each year?

 

[pka]

Here is problem:
View attachment 10784
Here is how I solved it:
View attachment 10785
Here is the solution in back of the book:
View attachment 10786
Now, how can this be? I mean, all you need to do is eyeball the formula and know that that x is going to be 12 to know that you are going to get a number larger than 360. So, what am I missing. I tried doing various things with the 6x^3/2 but no matter what I did I always got an answer that in no way conforms to that little 360.

You have failed to read carefully. It says that \(\displaystyle P\) is in the thousands.
\(\displaystyle P(x)=2x+6\sqrt{x^3}+700\) so that \(\displaystyle [P(16)-P(4)]K=[360]K=360,000\)
look here.

 

[Dr.Peterson]

You have failed to read carefully. It says that \(\displaystyle P\) is in the thousands.
\(\displaystyle P(x)=2x+6\sqrt{x^3}+700\) so that \(\displaystyle [P(16)-P(4)]K=[360]K=360,000\)
look here.

I think he understands the "thousands" part. I had the same thought at first, but then I saw that the reference to 360 implies the correct reading. The issue is in using 12 rather than 4 and 16.

 

[allegansveritatem]

You must be misreading the problem somehow. It doesn't say that x is the number of years elapsed, and P is the increase; rather, x is the number of years since 1980 for one specific year, and P is the population in that year. The answer does not involve x=12 at all. What you found is the population in 1992.

To find the increase from 1984 to 1986, you have to find the population in each year, and then subtract. What is x for each year? What is P for each year?

I see. P is not the increase but the total population at any one time and so the variable needs to be 4 and then 16. Then the results need to be subtracted.Right. I got 1992's population. I will work this out tomorrow. I have to read these problems more closely. Thanks.

 

[allegansveritatem]

You have failed to read carefully. It says that \(\displaystyle P\) is in the thousands.
\(\displaystyle P(x)=2x+6\sqrt{x^3}+700\) so that \(\displaystyle [P(16)-P(4)]K=[360]K=360,000\)
look here.

I'll have to try this out tomorrow. Thanks.

 

[allegansveritatem]

You have failed to read carefully. It says that \(\displaystyle P\) is in the thousands.
\(\displaystyle P(x)=2x+6\sqrt{x^3}+700\) so that \(\displaystyle [P(16)-P(4)]K=[360]K=360,000\)
look here.

By the way...what happened to the 700. I don't see it anywhere at wolfram alpha. I am just wondering.

 

[topsquark]

By the way...what happened to the 700. I don't see it anywhere at wolfram alpha. I am just wondering.

The 700 is a constant in the formula for P(x). So in finding the difference P(16) - P(4) the constant will cancel itself out. For example, (A + 700) - (B + 700) = A - B.

-Dan

 

[allegansveritatem]

The 700 is a constant in the formula for P(x). So in finding the difference P(16) - P(4) the constant will cancel itself out. For example, (A + 700) - (B + 700) = A - B.

-Dan

Good. Thanks

 

[allegansveritatem]

so, I went at this again and this is my result. I did not quite get 360, but 362. Not sure what to make of this but couldn't find the problem:

 

[Denis]

384 + 32 = 416, not 418.
Go stand in the corner for 32 minutes:cool:

 

[Steven G]

384 + 32 = 416, not 418.
Go stand in the corner for 32 minutes:cool:

The answer was off by just 2, so 2 minutes in the corner. That has been the standard rule for years. You young new comers think that you can come along and make up the rules here.

 

[Steven G]

384 + 32 = 416, not 418.
Go stand in the corner for 32 minutes:cool:

Woo hoo, you broke 1000 posts! I bet by March you'll catch up to me.

 

[Denis]

The answer was off by just 2, so 2 minutes in the corner. That has been the standard rule for years. You young new comers think that you can come along and make up the rules here.

Woo hoo, you broke 1000 posts! I bet by March you'll catch up to me.

....and then I'll leave you in my dust!!

 

[Steven G]

....and then I'll leave you in my dust!!

I always choose quality over quantity.

 

[allegansveritatem]

384 + 32 = 416, not 418.
Go stand in the corner for 32 minutes:cool:

Oh boy! Well, I probably had some wild idea flit through my harassed brain that that two and that 4 were meant to be multiplied rather than just married. Thanks for pointing it out.

 

[allegansveritatem]

The answer was off by just 2, so 2 minutes in the corner. That has been the standard rule for years. You young new comers think that you can come along and make up the rules here.

Yes, it was off by just two...but in this case that 2 is in the thousands column.