Question

Consider the demand function p=100(1.5⁻ᵠ). At a price of $48.00, what will be the quantity demanded?

Note: Enter your answer as a number only, without any special characters. Round your answer to 2 examples, if you determined that the answer is q=4.3311 enter this as follows: 4.33
Given the demand function p=55−2q, find the quantity that will maximize total revenue. Note: Enter your answer as a number only, without any special characters. For example, if you this as follows: 1000

Answer 1

The quantity demanded at a price of $48.00 is approximately 2.14.

Step-by-step explanation:

To find the quantity demanded at a given price, we can substitute the given price into the demand function and solve for the quantity. The demand function is given as p = 100(1.5^(-q)).

Substituting the given price of $48.00 into the equation, we have:

$48.00 = 100(1.5^(-q))

Dividing both sides by 100, we get:

0.48 = 1.5^(-q)

Taking the logarithm of both sides, we have:

log(0.48) = log(1.5^(-q))

Using logarithm properties, we can bring down the exponent:

log(0.48) = -q log(1.5)

Dividing both sides by log(1.5), we get:

-q = log(0.48) / log(1.5)

Finally, solving for q:

q = - (log(0.48) / log(1.5))

Using a calculator, we can find that q is approximately 2.14. Therefore, the quantity demanded at a price of $48.00 is approximately 2.14.