The true statement about the motorcycle's value is A, the initial value being $1200. Statements B, C, D, and E are false because they contain incorrect values or descriptions not supported by the given depreciation equation.
When analyzing the value of a motorcycle using the equation V(t) = 1200 - 85t, we can infer various pieces of information. Statement A is true, as the initial value of the motorcycle when new, V(0), is indeed $1200 since none of the value has depreciated.
For statement B, it is false because the initial cost is provided by the equation as $1200, not $850. Moving to statement C, after 2 years, or t=2, the motorcycle's worth is calculated as V(2)=1200 - 85(2) = 1200 - 170 = $1030, making this statement false as well.
For statement D, after 3 years, or t=3, we calculate V(3)=1200 - 85(3) = 1200 - 255 = $945, which indicates that this statement is false.
Lastly, statement E suggests the value of the motorcycle decreases by 85% each year which is false; it decreases by a fixed amount of $85 annually, not a percentage.
The probable question may be:
The equation represents the value of a motorcycle years after it was purchased. Which statements are also true of this situation? Select all that apply.
V(t)=1200−85t,
where V(t) is the value of the motorcycle t years after its purchase.
A. When new, the motorcycle cost $1200.
B. When new, the motorcycle cost $850.
C. After 2 years, the motorcycle is worth $867.
D. After 3 years, the motorcycle cost $782.
E. The value of the motorcycle is decreasing by 85% each year.
Additional Information:
The motorcycle's initial value is $1200.
The equation indicates a decrease in value over time, with a depreciation of $85 per year.
The cost mentioned in option D may be inaccurate based on the depreciation model.
The value after 2 years can be calculated by substituting t=2 into the equation.
Options:
A) True. The initial cost is $1200.
B) False. The initial cost is $1200, not $850.
C) True. Substitute t=2 into the equation: V(2)=1200−85×2=1030.
D) False. Substitute t=3 into the equation: V(3)=1200−85×3=945.
E) False. The value is decreasing by $85, not 85%.