A car was purchased for $36,730. The following equation can be used to predict the value of the car based on it age, where t stands for the time in years: A = 36730(.82)t.
If the car was purchased in March 2002, what will its value be in September 2009? Round your answer to the nearest dollar.
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To find the value of the car in September 2009, we need to substitute the value of t into the equation A = 36730(.82)t, where t represents the number of years since the car was purchased.
Given that the car was purchased in March 2002, we need to calculate the number of years between March 2002 and September 2009.
Here's how you can do it step by step:
1. Find the total number of years between March 2002 and September 2009.
- There are 7 full years between 2002 and 2009 (2003, 2004, 2005, 2006, 2007, 2008, 2009).
- Since the car was purchased in March 2002, we need to add a fraction of a year for the period from March to September in 2002.
- The fraction can be calculated by dividing the number of days from March to September by the number of days in a year (365 days).
- From March to September, there are 184 days.
- Therefore, the fraction of a year is 184 / 365 = 0.5041 (rounded to four decimal places).
2. Add the full years and the fraction of a year together.
- 7 + 0.5041 = 7.5041 (rounded to four decimal places).
3. Substitute the value of t into the equation A = 36730(.82)t.
- A = 36730(.82)(7.5041).
4. Calculate the value of A.
- A = 36730 * .82 * 7.5041 = 24596.59 (rounded to two decimal places).
Therefore, the value of the car in September 2009 would be approximately $24,597.