During a chemical reaction, the temperature T, in degrees Celsius, of a solution s seconds… — SAT

During a chemical reaction, the temperature $T$ , in degrees Celsius, of a solution $s$ seconds after the reaction begins is modeled by the equation $T = -0.04(s - 150) + 92$ , where $150 \le s \le 900$ . According to the model, how many minutes does it take for the temperature of the solution to decrease by $12$ degrees Celsius?

Cevap: 5 minutes

Cevap

To find the number of minutes it takes for the temperature to decrease by

12^\circ\text{C}

, we first determine the rate of temperature change from the linear model. The equation is given in the form

T = m(s - s_0) + T_0

, where the slope

m = -0.04

represents the rate of change of temperature in degrees Celsius per second. Thus, the temperature decreases at a rate of

0.04^\circ\text{C}

per second. To achieve a total decrease of

12^\circ\text{C}

, the time in seconds required is

\frac{12}{0.04} = 300

seconds. Converting

300

seconds to minutes gives

\frac{300}{60} = 5

minutes.

Adım Adım Çözüm

Identify the rate of change from the linear equation.

The rate of temperature decrease is

0.04^\circ\text{C}

per second.

The slope of the linear equation

T = -0.04(s - 150) + 92

-0.04

, which represents a change of

-0.04^\circ\text{C}

for every

1

second increase in time.

Calculate the time in seconds for a decrease of

12^\circ\text{C}

300

seconds

Divide the target temperature change of

-12^\circ\text{C}

by the rate of change of

-0.04^\circ\text{C}

per second:

\frac{-12}{-0.04} = 300

seconds.

Convert the time from seconds to minutes.

5

minutes

Since there are

60

seconds in

1

minute, divide

300

seconds by

60

\frac{300}{60} = 5

minutes.

Anahtar Kavram

Interpreting Linear Relationships in Context

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