Exercise · ZW-EXPONENTIAL-GROWTH-AND-DECAY-001 · ★☆☆ Basic
Solve \(y'=3y\) with \(y(0)=2\).
Choose one option.
Show answer
- A. \(y=2e^{3t}\)
Explanation
The general solution is \(y=y_0e^{kt}\) with \(k=3\) and \(y_0=2\).
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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