a) The sequence formed by the value at the beginning of each year is geometric. This is because the decrease in value each year is a constant percentage (10%), indicating a common ratio.
b) To find the explicit formula for the sequence, we start with the initial value of $1,250 and then multiply by the common ratio of 0.9 (100% - 10% = 90%) each year.
The explicit formula for the sequence is: $1,250 * (0.9)^n, where n represents the number of years.
c) To find the value of the computer at the beginning of the 6th year, we substitute n = 6 into the formula:
$1,250 * (0.9)^6 = $1,250 * 0.531441 = $664.30
Therefore, the computer will be worth $664.30 at the beginning of the 6th year.
Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
a) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
b) Write an explicit formula to represent the sequence.
c) Find the value of the computer at the beginning of the 6th year.
1 answer
1 answer