Decide whether the word problem represents a linear or exponential function. Then, write the equation of the function for a gym's customers who must pay $50 for a membership, plus... Decide whether the word problem represents a linear or exponential function. Then, write the equation of the function for a gym's customers who must pay $50 for a membership, plus $3 for each time they use the gym.
Understand the Problem
The question is asking whether the cost structure of a gym membership constitutes a linear or exponential function, and then requires the formulation of the corresponding equation based on the provided information about costs.
Answer
Linear; $y = 50 + 3x$
Answer for screen readers
Linear
$$ y = 50 + 3x $$
Steps to Solve
- Determine the Function Type
The problem states that there is a fixed cost of $50 for the membership and an additional variable cost of $3 for each gym visit. This cost structure is additive and does not multiply or compound, indicating it is a linear function.
- Identify Variables
Let:
- ( y ) = total cost
- ( x ) = number of times the gym is used
- Formulate the Equation
The total cost can be expressed as: $$ y = 50 + 3x $$
This equation shows that for every visit (each increment of ( x )), the total cost increases by $3, starting from a base membership cost of $50.
Linear
$$ y = 50 + 3x $$
More Information
This function represents a linear cost model because the total cost increases uniformly with each gym visit, which is characteristic of linear functions.
Tips
- Confusing linear functions with exponential functions by misinterpreting the relationship between costs and usage.
- Forgetting to account for the fixed membership fee when writing the equation.
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