Demand for your tie-dyed T-shirts is given by the formula
q = 490 − 100p^0.5
where q is the number of T-shirts you can sell each month at a price of p dollars. If you currently sell T-shirts for $15 each and you raise your price by $2 per month, how fast will the demand drop?
dq/dt = ______
Can anybody help me with this problem step by step? I don't know how to solve this or where to start. Thank you!
How fast will the demand drop?
2012-12-15 6:23 am
回答 (2)
2012-12-15 6:43 am
✔ 最佳答案
dq/dt = (-50 / sqrt(p)) * dp/dt <- Derivative in respect to time dp/dt = change in price of shirt = 2
dq/dt = demand rate change = ?
p = price of shirt = 15
dq / dt = -(50) / (sqrt(15)) * (2)
dq/dt = -(20 * sqrt(15)) / 3 = -25.82
2012-12-15 2:39 pm
dq/dt = dq/dp x dp/dt (chain rule)
= -50p^-0.5 x dp/dt
dp/dt = 2 as it means the rate of change in prices (the price change per month).
Thus dq/dt = -100p^-0.5.
When each shirts is $15, dq/dt = -100 x 1/sqrt(15) = -25.8 approximately.
Therefore, when each shirt costs $15, the quantity decreases by 26 units each month.
===================
By the way, a quantity is different from demand. A quantity equals q, but demand means a function, such as q = 490 - 100p^0.5. Hence, you may ask "How fast will the quantity (or the number of T-shirts) drop?".
= -50p^-0.5 x dp/dt
dp/dt = 2 as it means the rate of change in prices (the price change per month).
Thus dq/dt = -100p^-0.5.
When each shirts is $15, dq/dt = -100 x 1/sqrt(15) = -25.8 approximately.
Therefore, when each shirt costs $15, the quantity decreases by 26 units each month.
===================
By the way, a quantity is different from demand. A quantity equals q, but demand means a function, such as q = 490 - 100p^0.5. Hence, you may ask "How fast will the quantity (or the number of T-shirts) drop?".
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