The quantity demanded per month, x, of a certain make of personal computer (PC) is related to the average unit price, p (in dollars), of PCs by the equationx = f(p) =1009810,000 − p2It is estimated that t mo from now, the average price of a PC will be given byp(t) =4001 +18t+ 200 (0 ≤ t ≤ 60)dollars. Find the rate at which the quantity demanded per month of the PCs will be changing 16 mo from now. (Round your answer to one decimal place.)

The value of dx/dt is while the rate of change of quantity demanded per month after 16 months is 18.7.

Step-by-step explanation:

From the given data the equation of quantity demanded for average price is given as  is given as

The equation of average price p for a given value of t is given as

Now in order to determine the rate at which the quantity demanded will be changing is given as

This is found by using the chain rule as

Now

Now

So now the value of dx/dt is given as

So the value of dx/dt is

Now for the time =16 months price is given as

Now the value of x is given as

So the rate of change of quantity demanded per month after 16 months is 18.72

step-by-step explanation:

cats

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b