marmot
- 55
- 1
o my bro ahd an algebra 2 midterm and a question was this:
) A printer costs $35,000 (how old are these questions lol) but it depreciates 5% a year. What is the value by the 4th year?
ok so being an overtly complex person i tried to model a differential equation of this just for the kicks.
At first I thought
dP/dt=-0.05P
where P is price
and the solution is Po*exp(-0.5t) where Po=35000
however this is wrong. So I assumed I did not know r from dP/dt=-rP and worked the problem by finding the initial values.
so the solution gives me P=exp(-.051293t)Po which is correct.
I don't grasp intuitively the answer. why is dP/dt=.051293P when the problem says it goes down 0.5 each year so I assume P changes over time by -0.05P per year?
) A printer costs $35,000 (how old are these questions lol) but it depreciates 5% a year. What is the value by the 4th year?
ok so being an overtly complex person i tried to model a differential equation of this just for the kicks.
At first I thought
dP/dt=-0.05P
where P is price
and the solution is Po*exp(-0.5t) where Po=35000
however this is wrong. So I assumed I did not know r from dP/dt=-rP and worked the problem by finding the initial values.
so the solution gives me P=exp(-.051293t)Po which is correct.
I don't grasp intuitively the answer. why is dP/dt=.051293P when the problem says it goes down 0.5 each year so I assume P changes over time by -0.05P per year?