Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
Write an explicit formula to represent the sequence.
Find the value of the computer at the beginning of the 6th year.
(3 points)
The sequence formed by the value of the computer at the beginning of each year is geometric, because the value of the computer decreases by a constant percentage each year.
The explicit formula to represent the sequence is:
V(n) = $1,250 * (0.9)^n
Where n represents the number of years since Robin bought the computer.
To find the value of the computer at the beginning of the 6th year, we plug in n = 6 into the formula:
V(6) = $1,250 * (0.9)^6
V(6) = $1,250 * 0.531441
V(6) = $664.30
Therefore, the value of the computer at the beginning of the 6th year is $664.30.