Algebraic Modeling Worksheet
This worksheet focuses on developing algebraic models from real-world scenarios, including linear, quadratic, and exponential functions, and interpreting the models.
Includes
Standards
Topics
Algebraic Modeling
Name:
Date:
Score:
Read each question carefully and follow the instructions to develop and use algebraic models.
1. A taxi company charges a flat fee of $3.00 plus $2.50 per mile. Write a linear equation to model the cost (C) of a taxi ride for 'm' miles.
2. Using the equation from question 1, calculate the cost of a 10-mile taxi ride.
3. The height (h) of a projectile launched upwards is given by the equation h(t) = -16t² + 64t + 80, where 't' is the time in seconds. This is an example of a model.
4. In the equation h(t) = -16t² + 64t + 80, the coefficient -16 represents the effect of .
5. A population of bacteria doubles every hour. If you start with 50 bacteria, which equation models the population (P) after 'h' hours?
P = 50 + 2h
P = 50 * 2h
P = 50 * 2^h
P = 2 * 50^h
6. In a linear model y = mx + b, the 'b' represents the rate of change.
True
False
7. Consider the linear function y = 2x - 1. Plot at least three points and draw the line on the graph below.
8. A car's value depreciates by 15% each year. If a new car costs $25,000, write an exponential model for its value (V) after 't' years. Then, use your model to estimate the car's value after 3 years.
Related Worksheets
Radical Operations Worksheet
Grade 10 Math worksheet covering operations with radical expressions including simplification, addition, subtraction, multiplication, and division.
Solving Square Root Equations
This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 10 Algebra students.
Perfect Square Trinomials Worksheet
This worksheet focuses on identifying, factoring, and creating perfect square trinomials for Grade 10 Algebra students.
Mathematical Proofs: Introduction and Basic Techniques
This worksheet introduces fundamental concepts and techniques in mathematical proofs, suitable for Grade 10 students.
Three-Step Equations Worksheet
Solve three-step algebraic equations involving various operations for Grade 10 students.
Rearranging Equations Worksheet
A Grade 10 Math worksheet focused on rearranging algebraic equations to solve for specific variables.
Zero Product Property Worksheet
Practice applying the Zero Product Property to solve quadratic equations and other polynomial equations.
Parts of an Expression Review
This worksheet helps Grade 10 students identify and understand the different parts of algebraic expressions, including terms, coefficients, variables, and constants.