Chapter ISG, Problem 9.9.2.2P

a.

To determine

To find a function to represent $P(x)$ and $S(x)$ .

Answer to Problem 9.9.2.2P

Function of temperature of solution

  $S(x)=82-2.9(\frac{t}{3})$

Function of temperature of solution above lab temperature

  $P(x)=60-2.9(\frac{t}{3})$

Explanation of Solution

Given information:

  

Calculation:

Function of temperature of solution

  $S(x)=82-2.9(\frac{t}{3})$

Function of temperature of solution above lab temperature

  $P(x)=60-2.9(\frac{t}{3})$

t is the time

b.

To determine

To expain function is combination of two functions.

Answer to Problem 9.9.2.2P

Function is combination of linear and constant function

Explanation of Solution

Given information:

Function of temperature of solution

  $S(x)=82-2.9(\frac{t}{3})$

Calculation:

Function of temperature of solution

  $S(x)=82-2.9(\frac{t}{3})$

Here,

  $-2.9(\frac{t}{3})$ is linear function

  $82$ is constant function

Hence, function is combination of linear and constant function

c.

To determine

To find how long it will take until solution cool at ${45}^{\circ }C$ .

Answer to Problem 9.9.2.2P

  $t=16$ minutes

Explanation of Solution

Given information:

Function of temperature of solution above lab temperature

  $P(x)=60-2.9(\frac{t}{3})$

Calculation:

Function of temperature of solution above lab temperature

  $P(t)=60-2.9(\frac{t}{3})$

Put $P(t)={45}^{\circ }C$

  $45=60-2.9(\frac{t}{3})$

On solving,

  $2.9(\frac{t}{3})=60-45$

On solving,

  $2.9(\frac{t}{3})=15$

On solving,

  $t=\frac{15\times 3}{2.9}$

On solving,

  $t\approx 15.51$

On solving,

  $t=16$ minutes