Here are two functions that model the data: M(x)=1.53 x+114.8 F(x)=1.46 x+120.7 Use th

step 1 In part A here, we're looking to find the function that models the total US population. So that

Here are two functions that model the data: M(x)=1.53...

Here are two functions that model the data: $$\begin{array}{l}{M(x)=1.53 x+114.8} \\ {F(x)=1.46 x+120.7}\end{array}$$ Use the functions to solve Exercises 97–98. a. Write a function that models the total U.S. population for the years shown in the bar graph. b. Use the function from part (a) to fi nd the total U.S. population in 2005. c. Does the result in part (b) overestimate or underestimate the actual total U.S. population in 2005 shown by the bar graph? By how much?

Here are two functions that model the data:
$$\begin{array}{l}{M(x)=1.53 x+114.8} \\ {F(x)=1.46 x+120.7}\end{array}$$
Use the functions to solve Exercises 97–98.
a. Write a function that models the total U.S. population for the years shown in the bar graph.
b. Use the function from part (a) to fi nd the total U.S. population in 2005.
c. Does the result in part (b) overestimate or underestimate the actual total U.S. population in 2005 shown by the bar graph? By how much?

Key Concepts

Error Analysis

Error analysis in mathematical modeling involves comparing the predictions made by a model to actual observed data. This process helps identify whether the model overestimates or underestimates the real values and by how much, which is crucial for assessing the accuracy and reliability of the model and making any necessary adjustments.

Function Evaluation

Function evaluation is the process of substituting a specific input value into a function to determine its corresponding output. It is a critical skill in mathematics that helps in making calculations and predictions, such as finding the population at a particular year by plugging the year value into the function.

Modeling with Functions

Modeling with functions involves using mathematical expressions to represent real-world situations. In this context, linear functions are used to approximate data trends, such as population growth or changes over time, by capturing the underlying structure of the data. This technique allows predictions to be made and compared to actual observed values.

Linear Functions

A linear function is one that creates a straight line when graphed and is typically expressed in the form f(x) = mx + b, where m represents the slope (the rate of change) and b represents the y-intercept (the value of the function when x = 0). These functions are used to model situations where there is a constant rate of change, such as growth or decline over time.

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