Modeling With Functions Assignment

Question:

Answer: logarithmic - ratio

Question:

Answer: square root - ratio

Question: A bottle of water is placed in a freezer. The table shows how the approximate temperature of the bottle changes over time. What type of function best models the data in the graph?

Which exponential equation best models the data in the graph?

Answer: exponential - y=25(0.85)^5/5

Question: What type of function best models the data in the graph?

Which quadratic equation best models the data in the graph?

Answer: quadratic - y = 0.433x^2 (A)

Question: Which function best models the data in the table?

Which function best models the data in the table?

Answer: A - 120

Question: Which function best models the data in the graph?

The fulcrum of a lever is the point on which it turns. Based on the function, how many pounds of force are needed to lift the rock if the distance from the fulcrum is 6 feet?

Answer: y=60/x - 10

Question: Which function best models the data in the graph?

The horizontal reach of a fire hose is the distance the hose can spray water horizontally. Based on the function, about what is the minimum water pressure the fire hose needs to have a horizontal reach of 100 feet?

Answer: y=10.2 sqrtx - 96 lb/in.2

Question: Which type of function best models the data in the table? Justify your choice.

Answer: A quadratic function is the best model.

The data points are symmetric about the line x = 8.

The symmetry indicates the points might lie on a parabola.

Question: Which function best models the data in the graph?

What does the slope of the function represent in this situation?

What does the y-intercept of the function represent in this situation?

Answer: y=10.1 x+101 - the increase in pressure per meter of depth - the pressure at the ocean’s surface

Question:

Answer: y=(10)2^x/20 - greater by about 50 bacteria