Question 1087082
<font color="black" face="times" size="3">The value today is V = 100000 dollars when the time is t = 0, which is the starting time value. 
The value in 3 years, when t = 3, is V = 67681 dollars


So we have two ordered pairs (0,100000) and (3,67681). I'm going to treat t as x, and treat V as y. So each ordered pair goes from the form (t,V) to (x,y). Using the (x,y) form we can use the slope formula


First point = (x1,y1) = (0,100000)
Second point = (x2,y2) = (3,67681)
{{{m = (y[2] - y[1])/(x[2] - x[1])}}}
{{{m = (67681 - 100000)/(3 - 0)}}}
{{{m = (-32319)/(3)}}}
{{{m = -10773}}}


So the slope is {{{m = -10773}}} meaning that each year the value drops by $10,773


The y intercept is {{{b = 100000}}} because this is the starting value (at t = 0)


So we go from {{{y = mx+b}}} to {{{y = -10773x+100000}}}


The last thing to do is replace x with t and replace y with V(t) to get {{{V(t) = -10773t+100000}}}


Therefore the value function is {{{V(t) = -10773t+100000}}}


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Let's check the function. Plug t = 0 into the function to get
{{{V(t) = -10773t+100000}}}
{{{V(0) = -10773*0+100000}}}
{{{V(0) = 0+100000}}}
{{{V(0) = 100000}}}
So that matches with the fact the initial value is $100,000


Now plug in t = 3
{{{V(t) = -10773t+100000}}}
{{{V(3) = -10773*3+100000}}}
{{{V(3) = -32319+100000}}}
{{{V(3) = 67681}}}
Which matches with the value after 3 years. So the answer is confirmed</font>