Question

The temperatures t (in °f) at which water boils at selected pressures p (in pounds per square inch) can be modeled by t = 87.97 + 34.96 ln(p) + 7.91 p. Find the rate of change of the temperature (in degrees per pounds per square inch) when the pressure is 90 pounds per square inch. (Round your answer to two decimal places.)

Answer 1

The rate of change of temperature with respect to pressure when the pressure is 90 pounds per square inch is approximately 0.39 degrees per pound per square inch.

Step-by-step explanation:

The given model is t = 87.97 + 34.96 ln(p) + 7.91 p, where t represents temperature in °F and p represents pressure in pounds per square inch.

To find the rate of change of temperature with respect to pressure, we need to find d(t)/d(p). We can differentiate the given equation with respect to p to find this derivative.

d(t)/d(p) = 34.96/p + 7.91

Substituting p = 90 into the equation gives us:

d(t)/d(p) = 34.96/90 + 7.91

d(t)/d(p) ≈ 0.39 degrees per pound per square inch.