A certain vehicle loses 5% of its value each year. If the vehicle has an initial value of $24,742, construct a model that represents the value of the vehicle after a certain number of years. Use your model to compute the value of the vehicle at the end of 9 years.
To construct a model that represents the value of the vehicle after a certain number of years, we need to consider the initial value of the vehicle and the percentage decrease it experiences each year.
Let's start by understanding the decrease in value each year. The vehicle loses 5% of its value each year, which means that its value decreases by 5/100 * initial value = 0.05 * initial value each year.
Now, to construct the model, we can use the following formula:
Value after n years = Initial value * (1 - Percentage decrease) ^ n
In this case, the initial value is $24,742, and the percentage decrease is 5%. So, the model becomes:
Value after n years = $24,742 * (1 - 0.05) ^ n
Now, let's use this model to compute the value of the vehicle at the end of 9 years. Substitute n = 9 into the model:
Value after 9 years = $24,742 * (1 - 0.05) ^ 9
Calculating this expression will give us the value of the vehicle at the end of 9 years.
24742 (1 - .05)^y
plug in 9 for y