State whether each statement is true or false and briefly

he298c

he298c

Answered question

2021-08-11

State whether each statement is true or false and briefly explain why. If the statement is false, try to “fix it” by modifying the given statement to a new statement that is true. For exponential growth and decay, the rate of change is constant.

Answer & Explanation

averes8

averes8

Skilled2021-08-12Added 92 answers

In the case of exponential growth and decay, the rate of change is not constant.Thus, the statemant: For exponential growth and decay the rate of change is contant is false.
The general solution of differential equationy(t)=ky(t)With constant of proportionality k is calculated by separation of variables asy(t)y(t) dt =k dt That is1y dy =k dt 
ln|y|+c1=kt+c2
ln|y|=kt+cFory(t)>0
y(t)=Aekt(1)
HereA=ecFor k>0, equation (1) is exponential growth law and for k<0, equation (1) is exponential decay law.The rate of exponential growth and decay isy(t)=Akekt
Therefore, the true statement is: For exponential growth and decay the rate of change is y(t)=Akekt

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