A manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 1,500 + 3x. Answer the following questions.
How much would 2,000 items

Solution:

Given that,

The function is:

C(x) = 1500 + 3x

Where,

C(x) is the total cost

"x" is the number of manufactured items

How much would 2,000 items cost

Substitute x = 2000 in given function

C(2000) = 1500 + 3(2000)

C(2000) = 1500 + 6000

C(2000) = 7500

Thus 2000 items cost $ 7500

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3

(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.