Q1. Sales Analysis: Subscriber Growth Rate

Background

Topic: Applications of Derivatives in Business

This question tests your ability to apply calculus to model and analyze real-world business scenarios, specifically the rate of change of subscribers to a cable system over time.

Key Terms and Formulas

• : Number of subscribers (in thousands) after months

• : Subscriber function

• : Derivative of , representing the rate of change of subscribers per month

Step-by-Step Guidance

1. Recognize that is the derivative of a rational function. Use the quotient rule: .

2. Identify and . Compute and .

3. Apply the quotient rule to find , showing all steps but stopping before simplifying the final expression.

4. For part (B), substitute into and to set up the calculations, but do not compute the final values.

Try solving on your own before revealing the answer!

Q2. Medicine: Drug Concentration Rate in Bloodstream

Background

Topic: Applications of Derivatives in Medicine

This question tests your ability to use calculus to analyze how the concentration of a drug changes in the bloodstream over time.

Key Terms and Formulas

• : Drug concentration (mg/cm³) in the left arm after hours

• : Concentration function

• : Derivative of , representing the rate of change of concentration

Step-by-Step Guidance

1. Recognize that is the derivative of a rational function. Use the quotient rule: .

2. Identify (a constant) and . Compute and .

3. Apply the quotient rule to find , showing all steps but stopping before simplifying the final expression.

4. For part (B), substitute and into to set up the calculations, but do not compute the final values.

Try solving on your own before revealing the answer!