Final answer:
To estimate the price of the car in 2013, we use the compound interest formula with an initial price of $26,300, an annual inflation rate of 2.1%, over 7 years, resulting in an estimated price of approximately $30,400.
Step-by-step explanation:
The question asks to estimate the price of a type of car in 2013 given its price in 2006 with an annual inflation rate. To calculate this, we can use the formula for compound interest which is P(1 + r)^n, where P is the principal amount (initial price), r is the rate of interest (inflation rate), and n is the number of years. In this case, P is $26,300, r is 2.1% or 0.021, and n is 7 (from 2006 to 2013).
Using the formula:
- Price in 2013 = $26,300 * (1 + 0.021)^7
- Price in 2013 = $26,300 * (1.021^7)
- Price in 2013 ≈ $26,300 * 1.155 (rounded to three decimal places)
- Price in 2013 ≈ $30,369.50
This result should be reported with a number of significant figures consistent with the original price, which is $26,300. Therefore, the estimated price of the car in 2013, consistent with the given significant figures, is approximately $30,400.