Direct vs. Inverse Variation

Question

Also this one:
You purchase a new SUV; as age increases, the resale price decreases.
I believe this would be inverse, but the answer packet says neither direct nor inverse.

As I understand inverse, as one value goes up, the other goes down, which is exactly what this is doing???

Answer 1

you are right that value goes down with age
but
not directly or inversely
value is not equal to k t
and
value is not equal to k / t
in fact I need calculus to do it
change in V = k V * change in time
where k is less than one but positive, the rate of change is fast when new
or
dV/V = k dt
ln V = k t +constant
e^lnV = V = constant e^kt
constant is value when t = 0
V = Vi e^kt
if k is -.5
V = Vi e^-.5t for example
This is called exponential decay, in this case of car value but it could be a radioactive element losing a fraction of its protons every year.