Finding marginal demand if given demand and marginal price

[Imnotamathwiz94]

The annual demand q for bottles of wine from a vineyard when the bottles are priced at p dollars each satisfies the equation
qe0.03p = 4000.
The price is currently \$12 per bottle. Find the rate at which demand changes (with respect to time) if the price increases at a rate of \$1.20 per year.

 

[Imnotamathwiz94]

i don't understand what you mean

 

[MarkFL]

Hello and welcome to MHB, Imnotamathwiz94! :D

I split this post off of the topic in which it was originally posted. I also deleted the duplicate topic as it is not needed, but I know you must have realized it would be better to create your own topic, and did not know I was moving the post here.

Before we address the problem, I want to mention a few things about our forums here.

When using the dollar sign, you need to place a backslash directly in front of it, otherwise it parses as a $\LaTeX$ delimiter and will cause your post not to look like you intend. That's how I fixed your post above.

When you created the separate topic, you used a title which did not tell us anything we did not already know. Since you posted in the Calculus sub-forum, this already implies you want help with a calculus problem. Topic titles should indicate the nature of the problem being asked. This makes the forums more useful to everyone who browses them so they can see at a glance what type of problem is being discussed within each topic.

When you post a problem, we require you to show what you have already tried, or what your thoughts are on how to begin, such as relevant theorems. This way our helpers know where you are stuck or what you have done wrong, and can offer the best help possible.

Okay, you have stated a relationship between demand $q$ and price $p$. I am guessing that you omitted the exponentiation character, the caret "^". Is the relationship:

$$qe^{0.03p}=4000$$ ?

What is the problem asking you to find, in mathematical terms? What have you been given?

 

[Imnotamathwiz94]

ok thank you for that. I am new to this. the question is( Find the rate at which demand changes (with respect to time) if the price increases at a rate of $/1.20 per year. bottles/year

 

[MarkFL]

Hey, no worries, I just wanted to advise you so you would know and be able to post more effectively. :D

Okay, we are asked to find:

"the rate at which demand changes (with respect to time)"

How can we express this mathematically? How do we express rates of change?

 

[Imnotamathwiz94]

im not sure on what you mean

 

[MarkFL]

For example, if I wish to write a term that represents the rate of change of the area $A$ of a circle with respect to its radius $r$, I would write:

$$\frac{dA}{dr}$$

So, what would represent the rate of change of demand $q$ with respect to time $t$?

 

[Imnotamathwiz94]

Dq/dt

 

[Petrus]

$$\frac{dq}{dt}$$

Good (Yes)
So what does that mean? What should you do? write your function as q. So how does your function looks like?

 

[MarkFL]

Dq/dt

You should not capitalize the first differential, but you have the right idea.

Take your equation involving $q$, and differentiate with respect to $t$. Do you know how to do this?