vehicles lose value over time. A car is purchased for $23 500, but it is worth only $8750 after eight years. What is the average annual rate of change in the value of the car, as a percent?
change per year is (8750-23500)/8 = -1843.75
so, what's
-1843.75/23500?
Well, that car definitely experienced some depreciation drama over the years! Let's calculate the average annual rate of change and find out exactly how fast it lost its value.
To start, we need to find the decrease in value. The car was purchased for $23,500 and is now worth $8,750. So, the decrease is:
$23,500 - $8,750 = $14,750
Now, we'll divide this decrease by the number of years (8) to find the average annual decrease:
$14,750 / 8 = $1,843.75
Finally, let's calculate the percentage:
($1,843.75 / $23,500) x 100% = 7.85%
So, the average annual rate of change in the value of the car is approximately 7.85%. That's a lot of money going down the drain, or should I say, down the road!
To find the average annual rate of change in the value of the car as a percent, we can use the formula:
Rate of change = (Final value - Initial value) / Number of years
Given:
Initial value = $23,500
Final value = $8,750
Number of years = 8
Substituting these values into the formula, we get:
Rate of change = ($8,750 - $23,500) / 8
Rate of change = -$14,750 / 8
Rate of change = -$1,843.75
Since the rate of change is negative, we know that the value of the car is decreasing.
To express it as a percentage, we can find the percentage by dividing the rate of change by the initial value and multiplying by 100:
Percentage rate of change = (Rate of change / Initial value) x 100
Percentage rate of change = (-$1,843.75 / $23,500) x 100
Percentage rate of change = -0.0785 x 100
Percentage rate of change = -7.85%
Therefore, the average annual rate of change in the value of the car is approximately -7.85%.
To find the average annual rate of change in the value of the car as a percentage, you can use the formula for percent change.
The first step is to calculate the total change in value, which is the difference between the final value and the initial value:
Total change = Final value - Initial value
In this case, the final value is $8,750 and the initial value is $23,500, so:
Total change = $8,750 - $23,500
Next, you need to calculate the average annual rate of change. Since the time period is 8 years, you divide the total change by 8:
Average annual rate of change = Total change / Time period
In this case, the time period is 8 years, so:
Average annual rate of change = (Total change) / 8
Finally, to express the rate of change as a percentage, multiply the result by 100:
Average annual rate of change (in percentage) = (Average annual rate of change) * 100
Now let's do the calculations:
Total change = $8,750 - $23,500 = -$14,750
Average annual rate of change = -$14,750 / 8 = -$1,843.75
Average annual rate of change (in percentage) = -$1,843.75 * 100 ≈ -184.37%
Therefore, the average annual rate of change in the value of the car, as a percentage, is approximately -184.37%. Note that the negative sign indicates a decrease in value over time.