Constructing an exponential equation example | Algebra II | Khan Academy | Summary and Q&A

TL;DR
Liam's savings account increases by 20% each year. It will take 4 years for the account to reach $12,960.
Key Insights
- π Liam's savings account grows by 20% each year.
- π° The amount in Liam's account after t years can be represented by the equation 6,250 x 1.2^t.
- β It will take 4 years for the account to reach $12,960.
- βΊοΈ The equation for the situation is 12,960 = 6,250 x 1.2^t.
- β Multiple methods, such as brute force or logarithms, can be used to solve the equation.
- π By using logarithms, we find that t equals 4, indicating it will take 4 years for the account to reach $12,960.
Transcript
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Questions & Answers
Q: How much money will Liam have in his account after 2 years?
After 2 years, Liam will have $9,000 in his account. This is calculated by multiplying the amount he had at the end of 1 year ($7,500) by 1.2.
Q: What is the equation that represents the growth of Liam's account?
The equation that models the situation is 12,960 = 6,250 x 1.2^t. This equation represents the value of the account (12,960) when t years have passed.
Q: How can we solve the equation to find out how many years it will take for the account to reach $12,960?
To solve the equation, we can divide both sides by 6,250 and take the logarithm of both sides. Using logarithms, we find that t equals 4, meaning it will take 4 years for the account to reach $12,960.
Q: Can we solve the equation without using logarithms?
Yes, we can solve the equation by brute force or recognizing patterns. By multiplying 1.2 by itself four times, we get 2.0736, which is equal to 12,960 divided by 6,250. Therefore, it will take 4 years for the account to reach $12,960.
Summary & Key Takeaways
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Liam opened a savings account with $6,250 and it grows by 20% each year.
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After one year, Liam will have $7,500 in his account.
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The amount in Liam's account after t years can be calculated using the equation: 6,250 x 1.2^t.
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