Question

an employee at a garden center fills a water tank once a day around noon to a height of 20 inches. the function m models the height o the water in the tank, m(x), in inches, x seconds after 12:00 pm on monday as it fills.
describe the pattern of change of the graph.
the graph is increasing at a(n) increasing rate over a period of approximately 65 seconds.

Explanation:

Step1: Analyze the slope of the graph

The slope of a graph represents the rate of change. If the slope is positive, the function is increasing. If the slope is negative, the function is decreasing.

Step2: Observe the graph

Looking at the graph of \(M(x)\), as \(x\) (time) increases from \(0\) to approximately \(65\) seconds, the height \(M(x)\) is increasing. But the steepness of the graph (the slope) is decreasing. The slope of the tangent line to the curve at different points is getting less steep as \(x\) increases. So the function \(M(x)\) is increasing at a decreasing rate.

Answer:

increasing, decreasing