An airline offers daily flights between Chicago and Denver. The total monthly cost C (in millions of dollars) of these flights is modeled by $\sqrt { 0.2 x + 1 }$ , $\geq 0$ , where x is measured in thousands of passengers. The total cost of the flights in June is 2.8 million dollars. How many thousand passengers flew in June? Round your answer to the nearest thousand.

A) 19 thousands passengers
B) 44 thousands passengers
C) 34 thousands passengers
D) 39 thousands passengers
E) $9$ thousands passengers

Question

An airline offers daily flights between Chicago and Denver. The total monthly cost C (in millions of dollars) of these flights is modeled by

\sqrt { 0.2 x + 1 }

,

\geq 0

, where x is measured in thousands of passengers. The total cost of the flights in June is 2.8 million dollars. How many thousand passengers flew in June? Round your answer to the nearest thousand.

A) 19 thousands passengers
B) 44 thousands passengers
C) 34 thousands passengers
D) 39 thousands passengers
E)

9

thousands passengers

Zybrea Knight · Accepted Answer

Final Answer : C, Explanation :   To find the number of thousand passengers (x) that flew in June, we set the total cost C to 2.8 million dollars and solve for x in the equation   C = 0.2 x + 1 C = \sqrt{0.2x + 1} C = 0.2 x + 1 ​  . Plugging in 2.8 for C gives us   2.8 = 0.2 x + 1 2.8 = \sqrt{0.2x + 1} 2.8 = 0.2 x + 1 ​  . Squaring both sides of the equation to eliminate the square root gives us   7.84 = 0.2 x + 1 7.84 = 0.2x + 1 7.84 = 0.2 x + 1  . Solving for x, we subtract 1 from both sides to get   6.84 = 0.2 x 6.84 = 0.2x 6.84 = 0.2 x  , and then divide by 0.2 to find   x = 34 x = 34 x = 34  . Therefore, 34 thousand passengers flew in June.

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