A company bought a new
truck.
Each year the value of the
truck depreciates by 20%.
The value of the new truck
can be multiplied by a single
number to find its value at
the end of four years.
Find this single number as a
decimal.
To find the value of the truck at the end of four years, we need to multiply the initial value of the truck by the depreciation factor.
Since the truck depreciates by 20% each year, the value of the truck at the end of each year is 100% - 20% = 80% of its previous value.
Therefore, the single number we need to multiply the initial value by is 80% or 0.8.
So, the single number as a decimal is 0.8.
To find the value of the truck at the end of four years, we need to multiply its initial value by the depreciation factor for each year.
Step 1: Calculate the depreciation factor for each year.
Since the truck depreciates by 20% each year, the depreciation factor for each year would be (1 - 20%) = 0.8.
Step 2: Multiply the initial value of the truck by the depreciation factor for four years.
Let's assume the initial value of the truck is $100.
To find its value at the end of four years, we multiply $100 by the depreciation factor (0.8) four times.
$100 * 0.8 * 0.8 * 0.8 * 0.8 = $40.96.
Therefore, the single number that represents the value of the new truck at the end of four years is 0.4096 (40.96% of its initial value).
To find the value of the truck at the end of four years, we need to consider the depreciation rate of 20% per year.
To calculate this, we can multiply the value of the truck each year by the depreciation rate (80% of the previous year's value).
Let's denote the initial value of the truck as "V". After the first year, the truck's value will be 80% of V, or 0.8V. After the second year, the value will be 80% of 0.8V, or 0.8 * 0.8V = 0.64V. Similarly, after the third year, the value will be 80% of 0.64V, or 0.8 * 0.64V = 0.512V. Finally, after the fourth year, the value will be 80% of 0.512V, or 0.8 * 0.512V = 0.4096V.
Therefore, the single number that can be multiplied by the initial value of the truck to find its value at the end of four years is 0.4096, as a decimal.