Modeling with Functions Assignment

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

A - 120

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

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.

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?

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

Each place in a decimal number can be one of the digits 0 to 9. Each place in a binary number can only be 0 or 1. The table shows the number of digits needed to represent several decimal numbers as binary numbers. A logarithmic function is an appropriate model because, for evenly spaced y-values, the of consecutive x-values is constant.

logarithmic - ratio

What type of function best models the data in the graph? Which quadratic equation best models the data in the graph?

quadratic - y = 0.433x^2 (A)

The graph shows the relationship between the length, x, in meters, of a pendulum and its period, y, in seconds. The period is the amount of time it takes the pendulum to swing forward and back. An exponential function is not an appropriate model because, for evenly spaced x-values, the of consecutive y-values is not constant.

square root - ratio

Kirk made the graph to show his prediction of a population of bacteria over time. Which function best models the data in the graph? Jana predicts that the population, y, will grow according to y = 12 log(x + 1) + 10, where x is the time in minutes. How much greater does Kirk's model predict the population will be after 60 minutes than Jana's model?

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

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?

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

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?

y=10.2 sqrtx - 96 lb/in.2

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?

y=60/x - 10