Exercise · ZW-EXPONENTIAL-GROWTH-AND-DECAY-009 · ★★★ Advanced
If \(y'=ky\) with \(y(1)=6\) and \(y(3)=24\), what is \(y(0)\)?
Choose one option.
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- A. 3
Explanation
From \(e^{2k}=4\) we get \(e^k=2\), so \(y(0)=6/2=3\).
Review the concept: Exponential growth and decay
A quantity \(y\) with initial value \(y_0\) grows or decays exponentially when its rate of change is proportional to itself, with constant \(k\): it grows if \(k>0\), decays if \(k<0\).
\[y'=ky\;\Longrightarrow\; y(t)=y_0\,e^{kt}\]
More practice problems: exponential growth and decay
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