随着时间的推移呈指数增长 - 如何计算增量时间的增长?

发布于 2024-12-05 19:36:37 字数 90 浏览 2 评论 0原文

这可能是一个愚蠢的问题,但我仍然会问: 如果我在时间 0 处有一个初始值(在我的例子中始终为 1.0)和增长率,我如何计算出 Time1 和 Time2 之间的增量?

This is probably a silly / stupid question, but I'm still gonna ask it :
if I have an initial start value at Time 0 (which is in my case always 1.0) and a rate of growth, how do I figure out the increase between Time1 and Time2 ?

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青丝拂面 2024-12-12 19:36:37

Tn = T1 + 0.5(增长率)^2

这有意义吗?最后一项是增长率的平方的二分之一。

因此,时间段之间的差异为

diff(Tn - T1) = 0.5(增长率)^2

Tn = T1 + 0.5 (rate of growth)^2

Dose this make sense? The last term one half of the square of the rate of growth.

Thus the difference between the time periods is

diff(Tn - T1) = 0.5 (rate of growth)^2

旧街凉风 2024-12-12 19:36:37

增加 = 时间 2 的值 - 时间 1 的值。看似简单,其实很简单。该值等于 T0*(增长率)^Ti,其中 Ti 是您的时间。

increase = value at time2 - value at time1. Seems simple, is simple. The value is equal to T0*(rate of growth)^Ti, where Ti is your time.

囚我心虐我身 2024-12-12 19:36:37

如果我理解正确的话:

f(t2) - f(t1) where f(t) = initial * growth_factor^t

If i understand correctly:

f(t2) - f(t1) where f(t) = initial * growth_factor^t
谁的年少不轻狂 2024-12-12 19:36:37

如果您假设相对增长率r,则作为时间函数的值由下式给出

f(t) = exp(r*t)

(已合并f(0)=1f'(0 )=r),因此绝对差为,

D = f(t2) - f(t1) = exp(r*t2) - exp(r*t1)

而相对增量由下式给出

d = f(t2)/f(t1) - 1 = exp(r*t2)/exp(r*t1) - 1 = exp(r*(t2-t1)) - 1

If you assume a relative rate of growth r your value as a function of time is given by

f(t) = exp(r*t)

(already incorporated f(0)=1 and f'(0)=r) and thus the absolute difference is

D = f(t2) - f(t1) = exp(r*t2) - exp(r*t1)

while the relative increase is given by

d = f(t2)/f(t1) - 1 = exp(r*t2)/exp(r*t1) - 1 = exp(r*(t2-t1)) - 1
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