Linear versus exponential IRL word problems

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What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a function in which an independent variable appears in the exponent. It can be expressed in the form y = a(b^x), where a is a constant, b is the base, and x is the exponent.

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How do you identify a linear function from a word problem?

Back

A linear function can be identified by a constant rate of change, typically involving addition or subtraction. Look for phrases like 'per unit' or 'each time'.

Front

How do you identify an exponential function from a word problem?

Back

An exponential function can be identified by a variable that is multiplied by a constant factor repeatedly, often described with phrases like 'tripled' or 'doubled'.

Front

Write the equation for a linear function where a gym charges a membership fee and a per-use fee.

Back

y = 3x + 50, where y is the total cost, x is the number of uses, 3 is the per-use fee, and 50 is the membership fee.

Front

Write the equation for an exponential function where a bank account triples every month starting with $10.

Back

y = 10(3^x), where y is the amount in the account after x months.

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What does the slope represent in a linear function?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

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What does the base represent in an exponential function?

Back

The base represents the growth factor in an exponential function, indicating how much the quantity increases for each unit increase in x.

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If a library has 8000 books and adds 500 each year, what type of function is this?

Back

This is a linear function because the number of books increases by a constant amount each year.

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If a population of bacteria triples every hour, what type of function describes this growth?

Back

This is an exponential function because the population increases by a constant factor (tripling) over time.