A bank account balance grows at a rate that can be modeled by the exponential function , where y represents the balance and x represents the number of years. After 20 years, the balance will be approximately ________. (rounded to nearest whole number).
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to apply an exponential growth model to a real-world scenario. The key is to correctly substitute the given values into the exponential function and compute the result.
Key Concept Explanation
Exponential growth models are used to describe situations where the rate of change is proportional to the current quantity. In this case, the initial balance is 5000, and it grows by a factor of 1.03 each year.
Step-by-step Solution
1. Identify the given exponential function:
2. Substitute (since we are looking for the balance after 20 years):
3. Calculate :
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