Algebraic Modeling Worksheet
Grade 12 Algebraic Modeling worksheet covering linear, quadratic, exponential, and logarithmic models with real-world applications.
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Algebraic Modeling Worksheet
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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?
1 second
2 seconds
3 seconds
4 seconds
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.
True
False
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.