Question

math and graphing tutorial
the slope of the blue curve measures the planes rate of ascent. the unit of measurement for the slope of the curve is thousands of feet per minute.
at point a, the slope of the curve is, which means that the plane is at a rate of feet per minute. (hint: calculating the slope, pay extra attention to the units of analysis.)
at point b, the slope of the blue curve is, which means that the plane is at a rate of feet per minute. (hint: calculating the slope, pay extra attention to the units of analysis.)

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in the y - variable and $\Delta x$ is the change in the x - variable. Here, the y - variable is altitude (in thousands of feet) and the x - variable is time (in minutes).

Step2: Calculate slope at point A

At point A with coordinates $(6,30)$, we assume we can use the tangent line to approximate the slope of the curve. If we consider the units, the slope $m_A=\frac{30}{6}=5$. Since the altitude is in thousands of feet, the plane is ascending at a rate of $5\times1000 = 5000$ feet per minute.

Step3: Calculate slope at point B

Let's assume point B has coordinates $(2,5)$. The slope $m_B=\frac{5}{2}=2.5$. Since the altitude is in thousands of feet, the plane is ascending at a rate of $2.5\times1000=2500$ feet per minute.

Answer:

At point A, the slope of the curve is $5$, which means that the plane is ascending at a rate of $5000$ feet per minute.
At point B, the slope of the blue curve is $2.5$, which means that the plane is ascending at a rate of $2500$ feet per minute.