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Elden [556K]
3 years ago
8

he number of retro portable CD players you are prepared to supply to a retail outlet every week is given by the formula q = 0.1p

2 + 9p where p is the price it offers you. The retail outlet is currently offering you $100 per CD player. If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply? The supply will at a rate of CD players per week.
Mathematics
1 answer:
AlladinOne [14]3 years ago
3 0

Answer:

Supply will decrease at the rate of 29 CDs per week.

Step-by-step explanation:

The number of retro portable CD players prepared to supply to a retail outlet every week is represented by the formula

q = 0.1p²  + 9p

Here p = price offered

price it offers decreases at a rate of $1 per week.

In other words, \frac{dp}{dt}=(-$1) per week

Now we differentiate the given equation

\frac{dq}{dt}=\frac{d}{dt}(0.1p^{2}+9p )

\frac{dq}{dt}=[0.1(2p)+9]\frac{dp}{dt}

Since, \frac{dp}{dt}=(-$1) per week

\frac{dq}{dt}=(-1)[0.1(2p)+9]

For p = 100,

\frac{dq}{dt}=(-1)[(0.1\times 200)+9]

= (-1)[20+9]

= -29

Therefore, \frac{dq}{dt}=(-29)

Supply will decrease at the rate the rate of 29 CDs per week.

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