Question
Direct vs. Inverse Variation
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???
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???
Answers
Damon
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.
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.