A certain company was ordered to pay the cost of removing the waste products that it dumped into the river. That cost, C, in millions of dollars, of removing p% of the pollutants is found using the function C = 350p 100 − 1 . Which is an appropriate conclusion for this model?

A. It is very expensive to clean up a polluted river.
Incorrect. This statement may be true, but it is not a conclusion based on the function.

B. No company has the right to dispose of their waste into the water system.
Incorrect. This statement may be true, but it is not a conclusion based on the function.

C. The company will never be able to remove 100% of the waste from the river.
Correct! When p = 100, there would be a zero denominator. It is impossible to divide be zero.

D. It would cost $800 million dollars to remove 75% of the pollutants.
Incorrect. It would cost $1050 million ($1,050,000,000) to remove 75% of the pollutants.

In an effort to protect an endangered species of turtle, an environmental protection group introduced 125 turtles into a new beach in a state wildlife preserve. The population P of turtles is given by the function
P = 25(5 + 3t) 1 + 0.05t where t is the time in years. If the turtles continue to increase at the same rate forever, is there a maximum number of turtles that would call this beach “home”?

A. There is no maximum number of turtles. They would increase without end.
Incorrect. As the number of years increases toward infinity, the number of turtles goes to 1500.

B. There would be a maximum of 1500 turtles.
Correct! As the number of years increases toward infinity, the number of turtles goes to 1500.

C. There would be a maximum of 1300 turtles.
Incorrect. As the number of years increases toward infinity, the number of turtles goes to 1500.

D. There cannot be part of a turtle so there cannot be a maximum number of turtles.
Incorrect. It is true that there cannot be part of a turtle so only integer values work for the range. However, that fact has no effect on a maximum number of turtles.

A certain company uses a drill press to remove the core out of a metal cylinder to make it hollow. The height of the cylinder is a function of the radius, having the equation
h = 500 π(r² - 4). What is the range for this function as it pertains to this situation?

A. r > 2
Incorrect. r represents the radius whose values are the domain.

B. r > 0
Incorrect. r represents the radius whose values are the domain. Also, for r-values between 0 and 2, the height would be negative; for r = 2, the height would be undefined.

C. h < 500
Incorrect. With no minimum h-value, there would be negative heights. Also, there are many r-values that would give a height larger than 500 units.

D. h > 0
Correct! As the radius gets very large, the height gets closer to 0 units.

The chemist’s assistant needs to add pure acid to 20 milliliters of a solution that is 18% acid, using the function f(x) = 200(0.18) + x 20 + x . The percent of acid, f(x), is a function of x, the amount of the acid added. Which of the following is a reasonable conclusion?

A. If 21 ml of acid is added to the 20 ml of 18% acid solution, then the result would be 41 ml of a 60% acid solution.
Correct! By substituting 21 into the function for x, we get f(x) = (20(0.18) + 21)/(20 + 21) = 24.6/41 = 0.6 = 60%.

B. Adding 1 ml of pure acid will make the solution go from 18% to 25% acid.
Incorrect. Adding 1 ml of pure acid will make the solution go to 22% acid. f(x) = (20(0.18) + 1)/(20 + 1) = 4.6/21 = 0.219 = 22%.

C. Adding any amount of pure acid to the 20 ml of 18% acid solutions will make the resulting solution less acidic.
Incorrect. Adding any amount of pure acid to the 20 ml of 18% acid solutions will make the resulting solution more acidic.

D. Doubling the amount of the solution to 40 ml will double the amount of acid to 36%.
Incorrect. Doubling the solution to 40 ml means that 20 ml of pure acid would have been added to 20 ml of 18% acid. That situation would actually result in a 59% acid solution. f(x) = (20(0.18) + 20)/(20+20) = 23.6/40 = 0.59 = 59%.