Answer:
Step-by-step explanation: However, say that the car loses 50% of its value every year. This means that if you originally bought a car for 2,000 dollars in 2015, in 2016 it would be world 2,000/2=1,000, 1,000/2=500 the year after that, and so on. We can try to put this into a linear function, but it's hard to put it into one equation because we're not subtracting or adding to the cost of the car by a specific amount each year. If we had our equation as y=-0.5*x+2000, this wouldn't work because it's adding to the original amount, not multiplying. However, if we used an exponential equation such as y=b(m^a), with y representing the end cost, b representing the starting cost, m representing the amount multiplied per year, and a representing the number of years. This works because we start with a value, and multiply it by an amount each year. Since 50%=0.5, we plug that into m to get y=2,000(0.5^a). Therefore, this works well here. If the minivan were to depreciate by 3,000 every year, starting at $29,248, this means that we first have to find out what we multiply by 29,248 by the first year to subtract 3,000. As, after one year, the value is 29,248-3,000=26,248, we have 26,248=29,248(m^1). Therefore, we can divide 29,248 by both sides to get around 0.9 as our answer form. Thus, our equation is y=29,248(0.9^a). This type of equation would not work if we subtracted an amount every year because we're not multiplying by the same amount then. For example, if a toy was valued at 3$ and gained a value of one dollar every year, we could multiply the toy by 4/3 the first year to get 4, but the next year we wouldn't get 5.