Modeling with Functions Answers

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. Which type of function best models the data in the table? linear✔ logarithmicquadraticinverse variation

A logarithmic function is an appropriate model because, for evenly spaced y-values, the sumdifferenceproduct✔ ratio of consecutive x-values is constant.

What does the y-intercept of the function represent in this situation?the depth of the ocean floorthe pressure at the ocean floor✔ the pressure at the ocean’s surfacethe depth at which the pressure is 0

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. Which type of function best models the data in the graph?

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?

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

Which function best models the data in the table?

Which function best models the data in the graph?

Which function best models the data in the graph?

Which function best models the data in the graph?

Kirk made the graph to show his prediction of a population of bacteria over time. Which function best models the data in the graph?

An exponential function is not an appropriate model because, for evenly spaced x-values, the of consecutive y-values is not constant.

Which exponential equation best models the data in the graph?

Which quadratic equation best models the data in the graph?

beats per minute

pounds of force

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?

What does the slope of the function represent in this situation?the depth of the ocean floorthe pressure at the ocean’s surfacethe rate at which a diver’s depth is increasing✔ the increase in pressure per meter of depth

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?