A researcher uses the linear equation T = 18.5 + 4.2d to estimate the temperature, T, in d… — SAT

A researcher uses the linear equation $T = 18.5 + 4.2d$ to estimate the temperature, $T$ , in degrees Celsius, of the Earth's crust at a depth of $d$ kilometers below the surface in a certain region. What is the estimated increase in temperature, in degrees Celsius, for each increase of 5 kilometers in depth?

Answer: 21 degrees Celsius

Answer

The coefficient of

d

in the equation is

4.2

, representing a temperature increase of

4.2

degrees Celsius for every 1 kilometer increase in depth. To find the temperature increase for an increase of 5 kilometers in depth, multiply this rate of change by 5:

4.2 \times 5 = 21

Step-by-Step Solution

Identify the slope of the linear equation.

The slope is

4.2

In the equation

T = 18.5 + 4.2d

, the term

4.2d

indicates that for every 1 kilometer increase in depth (

d

), the temperature (

T

) increases by

4.2

degrees Celsius.

Calculate the total temperature increase for a 5-kilometer depth increase.

The increase is

21

degrees Celsius.

Since the rate of temperature increase is

4.2

degrees Celsius per kilometer, a depth increase of

5

kilometers results in a temperature increase of

4.2 \times 5 = 21

degrees Celsius.

Key Concept

Interpreting the slope of a linear equation in context as a constant rate of change.

Estimated Time:1m 30s

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