Algebraic Modeling Worksheet

Algebraic Modeling: Grade 11

Read each question carefully and provide the best answer. Show all your work for full credit.

1. Which type of function would best model the growth of a population that doubles every 10 years?

2. A projectile's height (h) in meters after t seconds is given by the function h(t) = -4.9t² + 20t + 5. What is the initial height of the projectile?

1. In a linear model, the rate of change is  .

2. The highest or lowest point of a quadratic function's graph is called the  .

3. An exponential function has a constant   factor.

1. A car rental company charges a flat fee of $30 plus $0.15 per mile driven. Write a linear equation to model the total cost (C) of renting a car for (m) miles.

2. Explain the difference between a growth factor and a decay factor in exponential models.

1. All real-world phenomena can be perfectly modeled by a single algebraic function.

2. The vertex of a parabola represents the maximum or minimum value of a quadratic function.

1. A company's profit (P) in thousands of dollars for selling (x) units of a product can be modeled by the function P(x) = -0.5x² + 50x - 300. a) What is the maximum profit the company can achieve? b) How many units must be sold to achieve this maximum profit? c) What are the break-even points (where profit is zero)?