If the unit price of the tire increases $2 per week, the demanded quantity decreases 167 tires per week.
The rate of change can be obtained by taking the derivative of the given function with respect to t (time).
The given equation is:
p + x² = 500
Where
p = price per unit
x = demanded quantity ( of a thousand)
The given parameter is: dp/dt = 2
x = 6
Taking the derivative with respect to t:
dp/dt + 2x . dx/dt = 0
2 + 2 . 6 . dx/dt = 0
dx/dt = -1/6
Since x unit is of a thousand, then
dx/dt = -1/6 x 1000 = -167 tires per week
Hence, if the unit price increases $2 per week, the demanded quantity decreases 167 tires per week.
Complete question:
Suppose the quantity demanded weekly of a certain type of tire is related to its unit price by the equation
p + x² = 500
where p is measured in dollars and x is measured in units of a thousand. How fast is the quantity demanded weekly changing when x = 6, and the price per tire is increasing at the rate of $2/week?
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