Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch).A model that approximates the data is Find the rate of change of T with respect to p when P = 20.Round
Your answer to two decimal places.

Question

Suppose the table below shows the temperature  at which a given liquid boils at selected pressures p (pounds per square inch).A model that approximates the data is  Find the rate of change of T with respect to p when P = 20.Round
Your answer to two decimal places.

Quizplus · Accepted Answer

We need to find $\frac{	ext{d}T}{	ext{d}p}$ when $p=20$.

From the given model, we have:

$T = 500+10p-\frac{1}{p}$

Differentiating both sides with respect to $p$, we get:

$\frac{	ext{d}T}{	ext{d}p} = 10+\frac{1}{p^2}$

Substituting $p=20$:

$\frac{	ext{d}T}{	ext{d}p}\bigg|_{p=20} = 10+\frac{1}{20^2} = 10.0025$

Rounding to two decimal places, we get:

$\frac{	ext{d}T}{	ext{d}p}\bigg|_{p=20} \approx 10.00$

Therefore, the best choice is B. Using the model given, we have:

$T(p)= -0.049p+212$

Taking the derivative with respect to $p$, we get:

$\frac{dT}{dp} = -0.049$

When $p=20$, we have:

$\frac{dT}{dp}\Big|_{p=20}=-0.049$

Rounding to two decimal places, we get $\frac{dT}{dp}\Big|_{p=20}\approx \boxed{-0.05}$ or $\boxed{B}$.

Suppose the Table Below Shows the Temperature at Which