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The value of a car decreases by 20 percent per year. Mr. Sing purchases a automobile. What is the value of the car at the end of the second year?
\$14,080
\$17,600
\$19,800
\$26,400
Studdy Solution
STEP 1
What is this asking? If a car loses 20% of its value each year, and it starts at , how much will it be worth after 2 years? Watch out! Don't forget that the car loses 20% of its *current* value each year, not 20% of the *original* value!
STEP 2
1. Calculate the value after the first year.
2. Calculate the value after the second year.
STEP 3
Alright, so Mr.
Sing buys this awesome car for .
That's our **initial value**!
STEP 4
It loses 20% of its value, which means it *keeps* 100% - 20% = 80% of its value.
So, the **rate of change** is 80% or .
STEP 5
To find the value after the first year, we **multiply** the **initial value** by the **rate of change**: So, after one year, the car is worth !
STEP 6
Now, for the second year, the **initial value** is the value after the first year, which is .
The car *still* loses 20% of its value each year, so the **rate of change** remains .
STEP 7
Again, we **multiply** the new **initial value** by the **rate of change**: Boom! After two years, the car is worth .
STEP 8
The value of the car at the end of the second year is .
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