Prove that if y = y^{0ekt}, where y_{0} and k

Kathy Williams

Kathy Williams

Answered question

2022-01-22

Prove that if y=y0ekt, where y0 and k are constants, then dydt=ky
(This says that for exponential growth and decay, the rate of change of the population is proportional to the size of the population, and the constant of proportionality is the growth or decay constant.)

Answer & Explanation

Jacob Homer

Jacob Homer

Beginner2022-01-22Added 41 answers

Given:
y=y0ekt
To prove:
dydt=ky
Consider,
y=y0ekt... (1)
where, y0 and k are constants.
Differentiating equation (1) w.r.t, t
dydt=ddt(y0ekt)
Taking constant out:
dydt=y0ddt(ekt)
=y0×ekt×k
From equation (1)y0ekt=y
dydt=yk
Hence the proof.
Cheryl King

Cheryl King

Beginner2022-01-23Added 36 answers

thank you for saving my soul

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