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, [tex]\frac{dp}{dt}=(-$1) per week[/tex]
Now we differentiate the given equation
[tex]\frac{dq}{dt}=\frac{d}{dt}(0.1p^{2}+9p )[/tex]
[tex]\frac{dq}{dt}=[0.1(2p)+9]\frac{dp}{dt}[/tex]
Since, [tex]\frac{dp}{dt}=(-$1) per week[/tex]
[tex]\frac{dq}{dt}=(-1)[0.1(2p)+9][/tex]
For p = 100,
[tex]\frac{dq}{dt}=(-1)[(0.1\times 200)+9][/tex]
= (-1)[20+9]
= -29
Therefore, [tex]\frac{dq}{dt}=(-29)[/tex]
Supply will decrease at the rate the rate of 29 CDs per week.
