Classifying Word Problems (Linear, Quad, Exp)

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What is a linear function?

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A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is a quadratic function?

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A quadratic function is a polynomial function of degree 2, typically expressed in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is an exponential function?

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An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent.

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How do you identify a linear word problem?

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A linear word problem typically involves constant rates of change, such as saving a fixed amount of money each month.

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How do you identify a quadratic word problem?

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A quadratic word problem often involves areas, projectile motion, or situations where the relationship between variables is not constant.

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How do you identify an exponential word problem?

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An exponential word problem involves growth or decay at a constant percentage rate, such as population growth or radioactive decay.

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Example of a linear equation from a word problem: Bob saves $40 per month. What is the equation?

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The equation is A(x) = 150 + 40x, where A is the amount in the account after x months.

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Example of a quadratic equation from a word problem: A rectangle has an area of 24 square units. What is the equation?

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Let the length be x and the width be x - 5. The equation is x(x - 5) = 24.

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Example of an exponential equation from a word problem: A culture of bacteria dies by 30% each year. What is the equation?

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The equation is N(t) = 5000(0.7)^t, where N is the number of bacteria after t years.

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What does the term 'decay' mean in exponential functions?

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Decay refers to a decrease in quantity over time, often expressed as a percentage reduction, such as a 30% decrease each year.