Final answer:
The question asks for the time it will take for a car to depreciate to half its value at a rate of 12% per year. To solve this, the exponential decay formula is used to find the number of years, which is then rounded to the nearest tenth.
Step-by-step explanation:
The question involves exponential decay (depreciation) to determine when Sandra's car, which depreciates at 12% per year, will be worth half its original price of $27,850. We can approach this by using the formula A = P(1 - r)^t, where A is the amount after depreciation, P is the original amount, r is the rate of depreciation, and t is the time in years. In this case, we're looking for t when A is half of P, that is, when A = $27,850 / 2, at a rate of r = 0.12 (12%).
To find t, the equation becomes $13,925 = $27,850(1 - 0.12)^t. Solving for t, t = ln($13,925/$27,850) / ln(1 - 0.12). Calculating this gives us the actual number of years after which the car's value will be halved, and rounding to the nearest tenth to comply with the question's requirements.