A submarine is diving toward the bottom of the ocean. The depth D of the submarine, in feet below sea level, after t minutes have elapsed is given by the function D(t)=20+16 t. The pressure, P, in pounds per square inch, exerted on the submarine at a depth of x feet is given by the function P(x)=14.7+0.445 x". " Which expression models the pressure exerted on the submarine as a function of the elapsed time, t, in minutes? Choose 1 answer: (A) 235.2+27.12 t (B) 23.6+7.12 t (C) 255.2+7.12 t (D) 8.9+21.82 t

Question

A submarine is diving toward the bottom of the ocean. The depth  D of the submarine, in feet below sea level, after  t minutes have elapsed is given by the function  D(t)=20+16 t. The pressure,  P, in pounds per square inch, exerted on the submarine at a depth of  x feet is given by the function  P(x)=14.7+0.445 x". " Which expression models the pressure exerted on the submarine as a function of the elapsed time,  t, in minutes? Choose 1 answer: (A)  235.2+27.12 t (B)  23.6+7.12 t (C)  255.2+7.12 t (D)  8.9+21.82 t

Bytelearn · Accepted Answer

Understand depth-time relationship: Understand the relationship between depth and time. The depth of the submarine after t minutes is given by the function D(t) = 20 + 16t. This means that the submarine starts at a depth of 20 feet below sea level and goes deeper by 16 feet for every minute that passes.Understand pressure-depth relationship: Understand the relationship between pressure and depth. The pressure exerted on the submarine at a depth of x feet is given by the function P(x) = 14.7 + 0.445x. This means that the pressure at sea level (0 feet depth) is 14.7 pounds per square inch, and for every foot the submarine goes deeper, the pressure increases by 0.445 pounds per square inch.Combine functions for pressure: Combine the two functions to express pressure as a function of time. To find the pressure as a function of time, we need to substitute the expression for depth as a function of time into the pressure function. This means we will replace x in P(x) with D(t) from the first function. P(t) = P(D(t)) = 14.7 + 0.445(D(t))Substitute depth into pressure function: Substitute D(t) into the pressure function. Now we substitute D(t) = 20 + 16t into the pressure function. P(t) = 14.7 + 0.445(20 + 16t)Distribute and simplify: Distribute 0.445 across the terms inside the parentheses. P(t) = 14.7 + 0.445 * 20 + 0.445 * 16t P(t) = 14.7 + 8.9 + 7.12tCombine terms for final expression: Combine like terms to simplify the expression. P(t) = 14.7 + 8.9 + 7.12t P(t) = 23.6 + 7.12t

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