Suppose that the number of a certain type of computer that can be sold when its price is P (in dollars) is given by a linear function N (P). (a) Determine N (P) if N (1000) = 10000 and N (1700) = 5800. (Use symbolic notation and fractions where needed.) N (P) = (b) Select the statement that gives the slope of the graph of N (P), including units and describes what the slope represents. 6 computers per dollar - 6 dollars per computer computers per dollar - 6 computers per dollar (c) What is the change AN in the number of computers sold if the price is increased by AP = 110 dollars? (Give your answer as a whole number.) AN = computers

a) N (P) = - 6P + 16000

b) slope = - 6 computers per dollar

That means the number of computer sold reduce by 6 per dollar increase in price.

c) ∆N = - 660 computers

Step-by-step explanation:

Since N (P) is a linear function

N (P) = mP + C

Where m is the slope and C is the intercept.

Case 1

N (1000) = 10000

10000 = 1000m + C ... 1

Case 2

N (1700) = 5800

5800 = 1700m + C ... 2

Subtracting equation 1 from 2

700m = 5800 - 10000

m = - 4200/700

m = - 6

Substituting m = - 6 into eqn 1

10000 = (-6) 1000 + C

C = 10000 + 6000 = 16000

N (P) = - 6P + 16000

b) slope = - 6 computers per dollar

That means the number of computer sold reduce by 6 per dollar increase in price.

Slope is the change in number of computer sold per unit Change in price.

c) since slope m = - 6 computers per dollar

∆P = 110 dollars

∆N = m * ∆P

Substituting the values,

∆N = - 6 computers/dollar * 110 dollars

∆N = - 660 computers.

The number of computer sold reduce by 660 when the price increase by 110 dollars