A scientist is measuring the temperature of a sample that is being heated at a constant ra… — SAT

A scientist is measuring the temperature of a sample that is being heated at a constant rate. At a starting time of $0$ minutes, the temperature of the sample is $12^\circ\text{C}$ . After $8$ minutes of heating, the temperature of the sample is $44^\circ\text{C}$ . If the temperature of the sample increases linearly with time, what is the temperature of the sample, in degrees Celsius, after $15$ minutes of heating?

Answer: 72 degrees Celsius

Answer

The rate of temperature change is

\frac{44 - 12}{8 - 0} = 4^\circ\text{C}

per minute. Using the slope-intercept form, the temperature

T

after

t

minutes can be represented by the function

T(t) = 4t + 12

. Substituting

15

for

t

yields

T(15) = 4(15) + 12 = 60 + 12 = 72

Step-by-Step Solution

Calculate the constant rate of temperature change (slope).

4 degrees Celsius per minute

To find how much the temperature increases each minute, divide the total change in temperature by the total change in time:

\frac{44 - 12}{8 - 0} = \frac{32}{8} = 4

Set up the linear function for temperature

T(t)

over time

t

T(t) = 4t + 12

The initial temperature at

t = 0

12^\circ\text{C}

, which represents the vertical intercept. The constant rate of change is

4^\circ\text{C}

per minute.

Find the temperature at

t = 15

minutes.

Substitute

15

for

t

in the equation:

T(15) = 4(15) + 12 = 60 + 12 = 72

Key Concept

Linear Functions and Rates of Change

Estimated Time:1m 0s

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