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Elanso [62]
2 years ago
14

The price p (in dollars) and the demand X for a particular clock radio are related by the equation X = 3000 -10p. Find and answe

r A - D

Mathematics
1 answer:
alukav5142 [94]2 years ago
6 0

The price p based on the equation given is p = 3000 - 0.1x.

<h3>How to express the price?</h3>

The equation given in the question is x = 3000 - 10p. The price(p) will be:

x = 3000 - 10p.

Make p the subject of the formula

x + 10p = 3000

10p = 3000 - x

p = (3000 - x)/10

p = 3000 - 0.1x

The revenue will be price multiplied by quantity. This will be:

= (3000 - 0.1x) × x

= 3000x - 0.1x²

The marginal revenue will be calculated after differentiating. This will be:

= 3000x - 0.1x²

= 3000 - 0.2x

The demand which is the quantity based on the information will be:

3000 - 0.2x = 0

0.2x = 3000

x = 1500

Learn more about demand on:

brainly.com/question/1245771

#SPJ1

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To see how much interest she'll get after a quarter:

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After two quarters:
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You can keep going until eventually reaching $8000 then see how many quarters has passed. That's a lot of calculator work!

There's another way that uses less calculation, but more algebra. I call it the exponential formula method! There's this general formula for stuff that increases exponentially, like virus, population, and MONEY:

m= d {e}^{tc}

M is money, d is deposit, t is time taken, and c is just some unknown constant related to the interest rate. There's also the natural logarithm form of this equation, which will come in handy later:

ln( \frac{m}{d} ) = tc

Alright first we gotta find that constant c for this equation to be useful! Let's plug in stuff we know.

ln( \frac{4331.16}{4132.79} ) = (0.25)c

We know how much she'll have after one quarter (0.25 years), and we know how much she deposited initially.

After pressing some buttons on the calculator we'll find that c = 0.1875.

Great! Now we can use that formula to find how many years (t) it'll take to reach M=$8000. To save time I'm going to use the natural log form:

ln( \frac{8000}{4132.79} ) = t(0.1875)

That will give us t = 3.522 which means it'll take approximately 3.5 years for her deposit to reach $8000!
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Step-by-step explanation:

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