Problem 120 - College Algebra Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The model \(P=-0.18 n+2.1\) describes the number of pay phones, \(P,\) in millions, \(n\) years after \(2000,\) so I have to solve a linear equation to determine the number of pay phones in 2010.

Step-by-Step Solution

Answer

The statement could be better worded. Instead of 'solving a linear equation', you are substituting a given value into the model and calculating the result.

Step 1: Understanding the statement

Read the statement carefully. In this case, the student needs to find out how many pay phones are predicted to be present in 2010 using the provided linear model.

Step 2: Analyzing the linear equation

The given linear equation is \(P=-0.18 n+2.1\). It is a model used for predicting the number of pay phones (in millions), n years after 2000. In this model, P is the number of pay phones, and n is the number of years after 2000. Since 2010 is 10 years after 2000, to find the predicted number of pay phones in 2010, you replace the variable n in the equation with 10.

Step 3: Substituting and solving the equation

After replacing n with 10, the model equation becomes \(P=-0.18*10+2.1\). Solving the equation will give the predicted number of pay phones in 2010.

Step 4: Verifying the sense of the statement

You can now see if the student's statement makes sense. The student doesn't have to 'solve a linear equation' in the traditional sense (as in, finding the value of an unknown variable). Instead, they need to substitute a given value into the linear model and compute the result. The original statement would have been better worded as 'I have to use the linear model to calculate the number of pay phones predicted in 2010.'.