Question

8 multiple choice 2 points the average temperature of the earth, measured in degrees celsius, can be modeled by the equation t(d)=0.03d + 10 degrees celsius where d is the depth below the earths surface, measured in meters. which of the following statements is true about this model? every additional 1 meter below the earths surface corresponds to an increase of 10°celsius of the earths temperature. every additional 1°celsius in temperature corresponds to an increase of 0.03 meters in depth. when the depth below the earth is 10 meters, the temperature has increased by 0.03°celsius. every additional 0.03 meter below the earths surface corresponds to an increase of 10°celsius of the earths temperature. every additional 1 meter below the earths surface corresponds to an increase of 0.03°celsius of the earths temperature. clear my selection

Explanation:

Step1: Analyze the linear - equation form

The equation $T(d)=0.03d + 10$ is in the form of a linear equation $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the context of the temperature - depth relationship, $m = 0.03$ represents the rate of change of temperature with respect to depth.

Step2: Interpret the slope

The slope $m=\frac{\Delta T}{\Delta d}=0.03$. This means that for every unit increase in $d$ (depth in meters), $\Delta T$ (change in temperature) is $0.03$ degrees Celsius. So, for every additional 1 meter below the Earth's surface, the temperature of the Earth increases by $0.03$ degrees Celsius.

Answer:

Every additional 1 meter below the Earth's surface corresponds to an increase of $0.03^{\circ}$ Celsius of the Earth's temperature.