Algebraic Modeling Worksheet

Algebraic Modeling Worksheet

Read each question carefully and provide clear, well-supported answers. Show all your work for full credit.

1. A taxi company charges a flat fee of $3.50 plus $2.25 per mile. Write a linear equation to model the cost (C) of a taxi ride based on the number of miles (m) traveled. Then, calculate the cost of a 15-mile ride.

2. The height (h) of a projectile launched upwards is modeled by the equation h(t) = -16t² + 96t + 10, where t is the time in seconds. At what time does the projectile reach its maximum height?

3. The population of a certain bacteria doubles every hour. If you start with 50 bacteria, the population after t hours can be modeled by the exponential function P(t) = 50 *  ^t. After 3 hours, the population will be   bacteria.

4. The Richter scale measures the magnitude of earthquakes using a logarithmic model. If an earthquake has a magnitude of R = log(I/I₀), where I is the intensity of the earthquake and I₀ is the intensity of a standard earthquake, how many times more intense is an earthquake with a magnitude of 7 compared to an earthquake with a magnitude of 5?

5. A dataset showing a constant rate of change between variables is best modeled by an exponential function.

6. Consider the function f(x) = x² - 4x + 3.

a) Sketch the graph of the function on the coordinate plane below.

b) Identify the x-intercepts and the y-intercept from your graph.