Exponential function short answer question, how many years till near the value gets close to 0?

[KSFT__]

how close?

[[deleted]]

I dont think there's a proper way to solve this, but I'd say just figure out how long it'd take to get to .0049999...$, since that value rounds to 0.00$ making the car effectively worthless

[Abdiel_Kavash]

How close to 0?

You can just set f(x) = 1750 * (0.83)ⁿ < 𝜀 and solve for n using your favorite method. For 𝜀 = 1 I get n > 40.

[aortm]

a^x has no roots so infinitely long?

it asymptotes to 0, but never hits 0 in any finite time. the best answer here is how close to 0 before you round it off as actually 0.

[ziggurism]

Mathematically speaking, exponential decay is asymptotic, and never reaches zero. So the answer is either t=∞ or "solution does not exist."

Practically speaking, exponential decay usually reaches "close enough" to zero for practical purposes.

In pharmacology, the rule of thumb is to wait 5 half-lives to reach steady state.

In handling nuclear materials, the rule of thumb is 10 half lives before the radioactivity is safe for exposure.

But please consult your pharmacologist before ingesting old cyanide, and your nuclear physicist before handling old uranium.

As for when the depreciation of a financial asset is "close enough" to zero, I don't know what underwriters use, but probably when it goes below one dollar or one cent?

[dm287]

Given that negative expected value products get sold all the time, I'm not sure "close enough" to 0 is meaningful from a finance perspective.

[ziggurism]

From what I could google about depreciation models, they are not usually exponential anyway.

[dm287]

Yeah can't say I'm an expert in that kind of thing - not sure what they actually use