Demand the demand function for a product is modeled by
p = 8000(1 - 5/5 + e-0.002x).
find the price p (in dollars) of the product when the quantity demanded is (a) x = 1000 units and (b) x = 2500 units, (c) what is the limit of price as x increases without bound?

a) 210.8 b) 10.77 c) 0

Step-by-step explanation:

a)p = 8000(1 - 5/5 + e^-0.002x).

when x = 1000 units

p = 8000 (  1 - (5 / (5 + e ^(-0.002 × 1000)))= 210.8

b) when x = 2500

p = 8000 (  1 - (5/(5 + e ^(-0.002 × 2500)))

p = 10.77

c) [/tex]

p = 8000 (  1 - (5/(5+ e^(-0.002∞)))

p = 8000 (  1 - (5 / (5+ e^-∞))

e^-∞ = 0

p =8000( 1- (5/5))

p = 8000 (1-1) = 0

the limit of price as x increase without bound reduces to zero

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.