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.
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? linearexponential✔ square rootinverse variation
An exponential function is not an appropriate model because, for evenly spaced x-values, the product✔ ratiosumdifference of consecutive y-values is not constant.
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?linearsquare root✔ exponentialinverse variation
Which exponential equation best models the data in the graph?
What type of function best models the data in the graph?linear✔ quadraticexponentialinverse variation
Which quadratic equation 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?
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? 74 lb/in.2✔ 96 lb/in.2102 lb/in.2126 lb/in.2
Which type of function best models the data in the table? Justify your choice.
The data is best modeled by an exponential function because the ratio between consecutive y-values is constant. As the x-values increase by a constant amount (1), each y-value is multiplied by a constant factor to get the next value, indicating a constant ratio rather than a constant difference.
Which did you include in your response?
Which function best models the data in the graph?
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
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
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