The marketing department of a textbook publisher finds that the demand for a book is related to the price according to the formula p=40-√(0.0001x+1),where x is the quantity of books sold (that is,the quantity demanded by the market) at price p.(A)If the demand is 1,000,000 books, what price should the publisher charge for the book? Use correct units in your answer and round your answer to the hundredth's place. (B)If the publisher charges $12.95 per book, how many books would they expect to sell?Use correct units in your answer and round your answer to the one's place.There are 2 parts a and b!Please help!!!! :(
what's the trouble? Just plug in your numbers!
p(1000000) = 40-√(0.0001*10^6+1)
= 40-√101
≈ 29.95
If p=12.95,
40-√(0.0001x+1) = 12.95
√(.0001x+1) = 27.05
.0001x+1 = 731.7025
x = 7,307,025
To find the price at which the publisher should charge for the book when the demand is 1,000,000 books, you need to substitute x = 1,000,000 into the given demand function p = 40 - √(0.0001x + 1).
(A) Let's start by substituting x = 1,000,000 into the formula:
p = 40 - √(0.0001 * 1,000,000 + 1)
p = 40 - √(100 + 1)
p = 40 - √101
To calculate the square root of 101, use a calculator or a math software:
√101 ≈ 10.0498756
Now, substitute this value back into the equation:
p = 40 - 10.0498756
p ≈ 29.95
Therefore, the publisher should charge approximately $29.95 for the book when the demand is 1,000,000 books.
Now let's move to part (B) to find out how many books the publisher would expect to sell when they charge $12.95 per book.
(B) To calculate the quantity of books they would expect to sell when the price is $12.95, we need to rearrange the demand formula and solve for x:
p = 40 - √(0.0001x + 1)
√(0.0001x + 1) = 40 - p
0.0001x + 1 = (40 - p)^2
0.0001x = (40 - p)^2 - 1
x = [(40 - p)^2 - 1] / 0.0001
Substituting p = $12.95 into the formula:
x = [(40 - 12.95)^2 - 1] / 0.0001
x = [(27.05)^2 - 1] / 0.0001
Now calculate (27.05)^2 using a calculator or math software:
(27.05)^2 ≈ 731.4025
Substitute this value back into the equation:
x = [731.4025 - 1] / 0.0001
x ≈ 7,314,025 - 1 / 0.0001
x ≈ 7,314,024 / 0.0001
x ≈ 73,140,240,000
Therefore, the publisher can expect to sell approximately 73,140,240,000 books when the price is $12.95 each.
Remember to round your answers to the specified decimal places as mentioned in the question.