Decide whether the word problem represents a linear or exponential function. Then, write the equation of the function. A bank account starts with $10. Every month, the amount of mo... Decide whether the word problem represents a linear or exponential function. Then, write the equation of the function. A bank account starts with $10. Every month, the amount of money in the account is tripled.
Understand the Problem
The question is asking whether the given word problem describes a linear or exponential function and requires the user to write the corresponding equation for the function. The problem states that a bank account starts with $10 and triples every month, suggesting an exponential growth scenario.
Answer
exponential $$ y = 10 \cdot 3^t $$
Answer for screen readers
exponential
$$ y = 10 \cdot 3^t $$
Steps to Solve
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Identify the type of function The problem describes a scenario where the amount of money triples every month. This indicates exponential growth rather than linear growth. In linear functions, the change is constant, while in exponential functions, the change increases by a constant factor.
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Define the variables Let ( y ) be the amount of money in the account after ( t ) months.
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Write the equation The general form for an exponential function is given by: $$ y = a \cdot b^t $$ Where:
- ( a ) is the initial amount (in this case, $10).
- ( b ) is the growth factor (which is 3, since the amount triples).
- ( t ) is the time in months.
Plugging in the known values, we get: $$ y = 10 \cdot 3^t $$
exponential
$$ y = 10 \cdot 3^t $$
More Information
This problem illustrates exponential growth, where the bank account balance triples each month, resulting in rapid increases in value over time.
Tips
- Mistaking exponential growth for linear growth. Remember that in exponential scenarios, the amount increases by a percentage each time period rather than a fixed amount.
- Forgetting to clearly identify the initial value and growth factor when writing the equation.
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