Need help with this Maths question please?

Iopu

A housing estate is modeled by the expression P = 500 + 100 - 50x2 (small upper 2)

What is the rate of change of the population of the estate at the end of the second year? (I think its the end of the first year in the expression)

At what year did the population reach a maximum?

What was the maximum population of the estate?

Any help would be appreciated I can't make any sense of this.

skippy1977

Should there be an x after the 100?

To find a rate of change we differentiate and to find the maximum we differentiate, let = 0 and solve for x.

Assuming there is an x after the 100 then the differentiate (rate of change) is 100-100x
Solving this we get x=1
and subbing this back into the population we get 500+100(1)-50(1)^2=550
Max Population is 550

Again this all depends on whether there is an x after the 100 in the original post.

If not sorry....

MathsManiac

The question is a bit nonsensical as asked.

Can you give us the exact and full text of the question?

Iopu

@skippy1977 Thank you very much for that. That helps a lot. There is supposed to be an x there.

@mathmaniac I will try to post the full question later on but I don't have access to a PC right now. I am on a smartphone and it would take me all day to type it in.

MathsManiac

Let's suppose that P represents the population of a housing estate. And let's suppose that x represents the time in years after some specified date.

My guess is that this was given in the question, right?

In that case, you need to know that the rate of change of a quantity is given by the derivative with respect to the time variable - in this case, dP/dx.

So, the first question requires you to find the value of dP/dx when x=2.

A function like this achieves its maximum at a point where the derivative is 0. (You should understand why that is so from your classwork / notes.

To find the maximum point, you need to find the value of x at which dP/dx = 0. This tells you when the maximum occurs. Once you know that, you can substitute it into the expression for P to find the maximum population.

Iopu

Thanks mathsmaniac.