Question 1087074
<font color="black" face="times" size="3">I think you meant to say "The depreciated value V" instead of "The depreciated value VV". I changed the VV to V. 


The value today is V = 100000 dollars when the time is t = 0, which is the starting time value. 
The value in 33 years, when t = 33, is V = 67681 dollars


So we have two ordered pairs (0,100000) and (33,67681). 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) = (33,67681)
{{{m = (y[2] - y[1])/(x[2] - x[1])}}}
{{{m = (67681 - 100000)/(33 - 0)}}}
{{{m = (-32319)/(33)}}}
{{{m = -10773/11}}}
{{{m = -979.3636}}} Use a calculator here. The decimal form is approximate (the '36' portion repeats forever)


So the slope is roughly {{{m = -979.3636}}}


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


So we go from {{{y = mx+b}}} to {{{y = -979.3636x+100000}}}


The last thing to do is replace x with t and replace y with V(t) to get {{{V(t) = -979.3636t+100000}}}


Therefore the value function is {{{V(t) = -979.3636t+100000}}}


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Let's check the function. Plug t = 0 into the function to get
{{{V(t) = -979.3636t+100000}}}
{{{V(0) = -979.3636*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 = 33
{{{V(t) = -979.3636t+100000}}}
{{{V(33) = -979.3636*(33)+100000}}}
{{{V(33) = -32318.9988+100000}}}
{{{V(33) = 67681.0012}}}
{{{V(33) = 67681.00}}}
Which matches with the value after 33 years. So the answer is confirmed


Side Note: if you use the fraction form for the slope then you won't run into rounding errors. The fact that we're rounding to 2 decimal places means that we don't have to worry about precision too much as long as the slope is expressed to 3 decimal places or more. You're probably wondering what the slope means? If so, then the slope is simply the rate of value decay or drop. In this case, the slope -979.3636 means the value V(t) is decreasing by $979.36 each year. The actual drop is a bit more than that but you can only round to the nearest hundredth for money problems like this.</font>