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Calculus / Calculus with Applications 10 / Chapter 4.4 / Problem 35E

Calculus with Applications | 10th Edition | ISBN: 9780321749000 | Authors: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

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Prove that if y = y0ekt, where y0 and k are constants,

Chapter 4, Problem 35E

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QUESTION:

Problem 35E

Prove that if y = y0ekt, where y0 and k are constants, then dy/dt = 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.)

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QUESTION:

Problem 35E

Prove that if y = y0ekt, where y0 and k are constants, then dy/dt = 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:

Solution:

Step 1 of 3:

In this question, we have to prove that if $y={y}_{0}{e}^{kt}$ y, where ${y}_{0}$ and $k\$ are constants, then $dy/dt=ky.$

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