Answer:
In the year of 2026.
Step-by-step explanation:
The value of the business furnite in t years after 2012 is given by an equation in the following format:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the value in 2012, and a is how much the value decreases a year.
If the value was $56,000 in 2012 and $48,500 in 2015
This means that [tex]V(0) = 56000, V(3) = 48500[/tex]
So
[tex]V(t) = V(0) - at[/tex]
[tex]48500 = 56000 - 3a[/tex]
[tex]3a = 7500[/tex]
[tex]a = \frac{7500}{3}[/tex]
[tex]a = 2500[/tex]
So
[tex]V(t) = 56000 - 2500t[/tex]
When will the value be $20,000?
t years after 2012, in which t is when V(t) = 20000. So
[tex]V(t) = 56000 - 2500t[/tex]
[tex]20000 = 56000 - 2500t[/tex]
[tex]2500t = 36000[/tex]
[tex]t = 14.4[/ttex]
This will happen in 14.4 years after 2012, so in the year of 2026.
