A submersible device is used for ocean research. The function g x = - 1 55 x + 19 x

Question

A submersible device is used for ocean research. The function g x = - 1 55 x + 19 x - 35 gives the depth below the surface of the ocean, in meters, of the submersible device x minutes after collecting a sample, where x &#62; 0 . How many minutes after collecting the sample did it take for the submersible device to reach the surface of the ocean?

Accepted Answer

The correct answer is 35 . It's given that the function g x = - 1 55 x + 19 x - 35 gives the depth below the surface of the ocean, in meters, of the submersible device x minutes after collecting a sample, where x > 0 . It follows that when the submersible device is at the surface of the ocean, the value of g x is 0 . Substituting 0 for g x in the equation g x = - 1 55 x + 19 x - 35 yields 0 = - 1 55 x + 19 x - 35 . Multiplying both sides of this equation by - 55 yields 0 = x + 19 x - 35 . Since a product of two factors is equal to 0 if and only if at least one of the factors is 0 , either x + 19 = 0 or x - 35 = 0 . Subtracting 19 from both sides of the equation x + 19 = 0 yields x = - 19 . Adding 35 to both sides of the equation x - 35 = 0 yields x = 35 . Since x > 0 , 35 minutes after collecting the sample the submersible device reached the surface of the ocean.

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