A server purchased at a cost of $108,000 in 2002 has a scrap value of $18,000 at the end of 5 years. Find the linear equation expressing the server's book value at the end of t years.
a- V(t)=108,000
b- V(t)=108,000t-18,000t
c- V(t)=18,000t+108,000
d- V(t)=18,000t
e- V(t)=18,000t-108,000
each year, 1/5 of lost value (10800-18000) is subtracted.
Or, note that 18K is 1/6 of 108K. That is, in 5 years it has lost 5/6 of its value: 1/6 per year.
Well, let's think about it. The book value of the server is decreasing over time as it gets older and loses value. So, the correct equation should have a negative coefficient for the time variable.
Now, at the end of 5 years, the server's book value is $18,000. So, we know that when t = 5, V(t) = $18,000.
Let's consider the options:
a- V(t) = 108,000 : This equation does not take into account the decrease in value over time, so it's not correct.
b- V(t) = 108,000t - 18,000t : This equation has both positive and negative coefficients for the time variable, which doesn't make sense. Also, it doesn't match the given information at t = 5.
c- V(t) = 18,000t + 108,000 : This equation has a positive coefficient for the time variable, which doesn't match the decreasing value. Also, it doesn't match the given information at t = 5.
d- V(t) = 18,000t : This equation has the correct negative coefficient for the time variable, and it matches the given information at t = 5. So, it's a possible answer.
e- V(t) = 18,000t - 108,000 : This equation has the correct negative coefficient for the time variable, but it doesn't match the given information at t = 5.
Therefore, the correct answer is d- V(t) = 18,000t
To find the linear equation expressing the server's book value at the end of t years, we need to determine the rate at which the value is decreasing over time.
Given that the server was purchased for $108,000 and has a scrap value of $18,000 after 5 years, we can calculate the rate of decrease by finding the difference between the initial value and the scrap value, and dividing it by the number of years.
Rate of decrease = (Initial value - Scrap value) / Number of years
= (108,000 - 18,000) / 5
= 90,000 / 5
= 18,000
Since the value decreases by $18,000 per year, the correct equation that expresses the server's book value at the end of t years is:
V(t) = Initial value - (Rate of decrease * t)
Substituting the values:
V(t) = 108,000 - (18,000 * t)
Therefore, the correct answer is:
e- V(t) = 18,000t - 108,000
To find the linear equation expressing the server's book value at the end of t years, we need to determine the rate at which the book value decreases over time.
We know that the server was purchased at a cost of $108,000 in 2002. This initial value allows us to calculate the rate of decrease in value over time. Since the server has a scrap value of $18,000 at the end of 5 years, the decrease in value over 5 years is given by:
Decrease = Cost - Scrap Value
Decrease = $108,000 - $18,000
Decrease = $90,000
The rate of decrease can be calculated by dividing the total decrease by the number of years:
Rate of decrease = Decrease / Number of Years
Rate of decrease = $90,000 / 5 years
Rate of decrease = $18,000/year
Therefore, the linear equation expressing the server's book value at the end of t years is:
V(t) = Initial Value - Rate of decrease * t
Substituting the values we know:
V(t) = $108,000 - $18,000 * t
Hence, the correct answer is (e): V(t) = 18,000t - 108,000.