10.6 Applications  (Page 3/4)

A study of the air quality in a particular city by an environmental group suggests that $t$ years from now the level of carbon monoxide, in parts per million, in the air will be

$A=0.2t^2+0.1t+5.1$

(a) What is the level, in parts per million, now?

(b) How many years from now will the level of carbon monoxide be at 8 parts per million? Round to the nearest tenth.

A contractor is to pour a concrete walkway around a swimming pooi that is 15 feet wide and 25 feet long. The area of the walkway is to be 276 square feet. If the walkway is to be of uniform width, how wide should the contractor make it?

The manufacturer of electronic fuel injectors determines that the number $N$ of injectors sold is related to the price $x$ per injector by $N=22x-x^2.$ At what price should the manufacturer price the injectors so that 112 of them are sold?

The owner of a stained-glass shop determines that the number $N$ of pieces of a particular type of glass sold in a month is related to the price $x$ per piece by $N=21x-x^2.$ At what price should the shop buyer price the glass so that 162 sell?

It is estimated that $t$ years from now the population of a certain city will be

$P=t^2-15t+12,036$

(a) What is the population now?

(b) How many years from now will the population be 12,000?

It is estimated that $t$ years from now the population of a certain city will be

$P=t^2-16t+24,060$

(a) What is the population now?

(b) How many years from now will the population be 24,000?

If an object is thrown vertically upward, its height $h$ , above the ground, in feet, after $t$ seconds is given by $h=h_0+v_{0}t-16t^2$ , where $h_0$ is the initial height from which the object is thrown and $v_0$ is the initial velocity of the object. Using this formula and an approach like that of Sample Set A, solve this problem.

A ball thrown vertically into the air has the equation of motion $h=48+32t-16t^2.$

(a) How high is the ball at $t=0$ (the initial height of the ball)?


(b) How high is the ball at $t=1$ (after 1 second in the air)?


(c) When does the ball hit the ground? ( Hint: Determine the appropriate value for $h$ then solve for $t$ .)