Question

assume the following situation can be modeled by a linear function. write an equation for the linear function and use it to answer the given question. be sure you clearly identify the independent and dependent variables. then briefly discuss whether a linear model is reasonable for the situation described.

the price of a particular model car is $21,000 today and rises with time at a constant rate of $930 per year. how much will a new car of this model cost in 3.9 years?

select the correct choice below and fill in the answer box to complete your choice.
(simplify your answer.)

a. the independent variable is the price (p), in dollars, and the dependent variable is time (t), in years. the linear function that models this situation is t =
b. the independent variable is time (t), in years, and the dependent variable is the price (p), in dollars. the linear function that models this situation is p =

Explanation:

Identify variables and model type

Using the Independent and Dependent Variables and Linear Growth knowledge points

• Independent variable: time \(t\), in years
• Dependent variable: price \(p\), in dollars
• Initial value (y-intercept): \(21000\)
• Constant rate of change (slope): \(930\)

Formulate the linear equation

Using the Linear Growth knowledge point

$$ p = 930t + 21000 $$

Evaluate the correct option

Using the Independent and Dependent Variables knowledge point

• Option A states the independent variable is price \(p\) and dependent is time \(t\), which is incorrect.
• Option B states the independent variable is time \(t\) and dependent is price \(p\), with the function \(p = 930t + 21000\), which is correct.

Answer:

• (A) The independent variable is the price (p), in dollars, and the dependent variable is time (t), in years. The linear function that models this situation is t =
• (B) The independent variable is time (t), in years, and the dependent variable is the price (p), in dollars. The linear function that models this situation is p = \(930t + 21000\) (Correct answer)