6. Linear Systems and Modeling

Linear Modeling — Quiz

Test your understanding of linear modeling with 5 practice questions.

Practice Questions

Question 1

A linear model is developed to predict the amount of medication remaining in a patient's bloodstream ($M$) in milligrams, $t$ hours after administration. If the initial dosage is $400$ mg and the medication is metabolized at a constant rate of $20$ mg per hour, which equation accurately represents this model?

Question 2

A financial analyst uses a linear model to predict a company's quarterly revenue ($R$) in millions of dollars, based on its advertising expenditure ($A$) in thousands of dollars. If the model is given by $R = 0.5A + 10$, what is the predicted increase in revenue for every additional $$10,000 spent on advertising?

Question 3

A scientist models the growth of a bacterial colony. The population ($P$) in thousands, $h$ hours after an experiment begins, is given by the linear equation $P = 15h + 200$. If the population reaches $350$ thousand, how many hours have passed since the experiment began?

Question 4

A linear model is used to describe the relationship between the number of units produced ($x$) and the total production cost ($C$) in dollars. If the cost to produce $50$ units is $$1200$ and the cost to produce $100$ units is $$2000, what is the fixed cost (cost when $x=0$)?

Question 5

A linear model predicts the value ($V$) of a car in dollars after $t$ years. If a car initially costs $$25,000$ and depreciates at a constant rate of $$2,000 per year, what will be the car's value after $7$ years?