Algebra Answers

A new smartphone can be purchased for $840. The phone’s value has a half-life of 23 months and can be modelled by the function 

𝑉 = 840(0.5) 𝑡/23

Algebraically determine how long, to the nearest tenth of a month, it takes the smartphone to be worth $601

1.     A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest? Also, find a rigorous algebraic solution for the problem.

A water cooler holds 25 liters of sports drink. Approximately how many gallons is this? (1 gallon = 3.785 liters)

Create a cubic polynomial inequality for which 𝑥 = 0 or 𝑥 ≥ 5 is the solution. Explain your answer fully using terminology learned in this unit and a diagram.

Explain the difference between round and hard brackets when expressing intervals. Use an example to justify

When a polynomial is divided by x + 1, the remainder is 5. When the same polynomial is divided by x – 1, the remainder is 1. When the same polynomial is divided by x – 2, the remainder is 20. Determine the remainder when the polynomial is divided (x + 1)(x – 1)(x – 2).

Consider the polynomial function 𝑃(𝑥) = 2𝑥^3 − 𝑚𝑥^2 + 𝑥 − 5𝑚. The remainder when P(x) is divided by (𝑥 − 2) is four times the remainder from dividing P(x) by (𝑥 + 1). Determine m algebraically and show all your work. 

Consider the polynomial function 𝑃(𝑥) = 2𝑥^3 − 𝑚𝑥^2 + 𝑥 − 5𝑚. The remainder when P(x) is divided by (𝑥 − 2) is four times the remainder from dividing P(x) by (𝑥 + 1). Determine m algebraically and show all your work. 

Find the producer's surplus at Q = 9 for the following supply functions:

(a) P = 12 + 2Q

(b) P = 20√Q + 15