Exercise · ZW-EXPONENTIAL-GROWTH-AND-DECAY-008 · ★★☆ Intermediate
With \(y'=0.1y\), about when does the quantity triple?
Choose one option.
Show answer
- D. 11.0
Explanation
Solve \(e^{0.1t}=3\): \(t=\ln3/0.1\approx11.0\).
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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