Mathematics: The value of business furniture is assumed to depreciate (decrease) in value linearly. If the value was $56,000 in 2012 and $48,500 in 2015, when will the value be $20,000? Setup an equation for the value and solve algebraically.

The value of business furniture is assumed to depreciate

bullockarwen

19.01.2022

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:

V(t) = V(0) - at

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 V(0) = 56000, V(3) = 48500

V(t) = V(0) - at

48500 = 56000 - 3a

3a = 7500

$a = \frac{7500}{3}$

a = 2500

V(t) = 56000 - 2500t

When will the value be $20,000?

t years after 2012, in which t is when V(t) = 20000. So

V(t) = 56000 - 2500t

20000 = 56000 - 2500t

2500t = 36000

[tex]t = 14.4[/ttex]

This will happen in 14.4 years after 2012, so in the year of 2026.

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