Question

Suppose the supply function for x units of a product at a price of p dollars is given by p=10+5ln(3x+1). How many units of this product would be supplied when the price is $50?

Answer 1

x = 993.32

Step-by-step explanation:

Given:

p=10+5ln(3x+1) , where p = $50

50 = 10 + 5ln(3x+1)

50-10 = 5ln(3x+1)

40 = 5ln(3x+1)

40/5 = ln(3x+1)

8 = ln(3x+1)

3x + 1 =
`e^(8)`

Using calculator
`e^(8)` = 2,980.96

3x + 1 = 2,980.96

3x = 2,980.96 - 1

3x = 2,979.96

x = 2,979.96 / 3

x = 993.32

Therefore, 993.32 units would be supplied.