Referencing the exponential function D(t)=1,000⋅(0.90)^t for the asset's depreciation, what does the horizontal asymptote of the graph represent in this scenario?
Answer
A
The asset will maintain a minimum value of 1 dollars comma 000 indefinitely.
B
The asset's value will eventually decline to zero.
C
The asset's value will increase after reaching the horizontal asymptote.
D
The asset's value will eventually stabilize at a certain level.
Explanation
Since 0.90 is between 0 and 1, the value is multiplied by 0.90 each time period and gets smaller. As t increases, D(t) approaches the horizontal asymptote y = 0, so the asset’s value will eventually decline toward zero. It does not reach zero at any finite time.
AI-written and checked against the verified answer.