Algebraic Modeling Worksheet

This worksheet focuses on developing algebraic models from real-world scenarios, including linear, quadratic, and exponential functions, and interpreting the models.

Grade 10 Math AlgebraAlgebraic Modeling

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSA.CED.A.1CCSS.MATH.CONTENT.HSA.CED.A.2CCSS.MATH.CONTENT.HSF.LE.A.1

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AlgebraModelingFunctionsGrade 10

8 sections · Free to use · Printable

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Algebraic Modeling

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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.