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Math  /  Algebra

QuestionState whether the decay is linear or exponential, and answer the associated question. The value of a car is decreasing by 8%8 \% per year. If the car is worth $12,000\$ 12,000 today, what will it be worth in two years?
State whether the decay is linear or exponential. The decay is □\square since the quantity decreases by the same □\square amount.

Studdy Solution

STEP 1

1. The car's value decreases by a percentage each year.
2. The initial value of the car is $12,000.
3. We need to determine the type of decay and calculate the car's value in two years.

STEP 2

1. Determine the type of decay.
2. Calculate the car's value after one year.
3. Calculate the car's value after two years.

STEP 3

The decay is exponential since the quantity decreases by the same percentage amount each year.

STEP 4

Calculate the car's value after one year. The car's value decreases by 8%8\% each year, so the remaining value after one year is 100%−8%=92%100\% - 8\% = 92\%.
Calculate 92%92\% of the current value: Value after one year=0.92×12,000=11,040. \text{Value after one year} = 0.92 \times 12,000 = 11,040.

STEP 5

Calculate the car's value after two years. Apply the same 8%8\% decrease to the value after one year.
Calculate 92%92\% of the value after one year: Value after two years=0.92×11,040=10,156.80. \text{Value after two years} = 0.92 \times 11,040 = 10,156.80.
The car will be worth $10,156.80\$10,156.80 in two years.

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