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What gives the relationship between the measurements on a drawing or model and the measurements of a real object?
It is a matter of scale.
Which pairs of real-world data offers models of exactly one exponential relationship and one linear relationship?
One example of an exponential relationship is the growth of bacteria in a controlled environment, where the population doubles at regular intervals. In contrast, a linear relationship can be observed in the distance traveled by a car moving at a constant speed over time. In both cases, the exponential model captures rapid growth, while the linear model illustrates steady, uniform change.
How do you model 1.04 on a grid?
To model 1.04 on a grid, you can represent it as a square with side lengths of 1 and 0.04 units. This can be visualized as a square divided into 100 smaller squares, with 4 of those smaller squares shaded to represent the 0.04 part. Each smaller square would represent 0.01. This grid model can help demonstrate the concept of decimals and their relationship to whole numbers.
When does it make sense to chose a linear function to model a set of data?
If a linear model accurately reflects the measured data, then the linear model makes it easy to predict what outcomes will occur given any input within the range for which the model is valid. I chose the word valid, because many physical occurences may only be linear within a certain range. Consider applying force to stretch a spring. Within a certain distance, the spring will move a linear distance proportional to the force applied. Outside that range, the relationship is no longer linear, so we restrict our model to the range where it does work.
What is meant by mathematical model in particular linear programming model?
A mathematical model is the representation of a relationship or state or phenomenon in a mathematical form using control variables.
