Question

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

Answer 1

110

Explanation:

Answer 2

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

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