Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 8p cubedplusx squaredequals45 comma 225. Determine the rate at which sales are changing at a time when xequals135, pequals15, and the price is falling at the rate of $.60 per week.

The value of rate at which the sales are changing is 12

Step-by-step explanation:

Given function is,

To determine the rate at which sales are changing, that is, , differentiate given function with respect to t,  

Applying sum rule of derivative,

Applying power rule and constant rule of derivative,

Substituting the values,  

Since it is given that price is falling, so is negative.

Adding -3240 from both sides,

Dividing by 270,

.25

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.