Final answer:
To find the number of units supplied at $66 per unit using the given supply function, substitute the price into the equation, isolate the quantity variable, and solve. The resulting quantity is then rounded to the nearest whole number.
Step-by-step explanation:
The task is to determine how many units of a product would be supplied at a price of $66 per unit based on the supply function p = 18 + 6 ln(4x + 1). To find the quantity supplied, x, substitute p = $66 into the supply equation and solve for x.
Starting with the equation:
66 = 18 + 6 ln(4x + 1)
Subtract 18 from both sides:
48 = 6 ln(4x + 1)
Divide by 6:
8 = ln(4x + 1)
Now, use the inverse of the natural logarithm, which is the exponential function e, to solve for x:
e³ = 4x + 1
4x = e³ - 1
x ≈ (e³ - 1) / 4
Calculate the value and round to the nearest whole number to obtain the quantity supplied.