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Q81.

Expert-verified
Found in: Page 418

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

After the switch is closed in the circuit shown, the current $t$ seconds later is $I\left(t\right)=0.8{e}^{-3t}\mathrm{sin}10t$. Find the current at the times,(a). $t=0.1\text{s}$(b). $t=0.5\text{s}$

The value of the function at $t=0.1$ and $t=0.5$is $0.49870$ and $-0.20906$.

See the step by step solution

Step 1: Given information.

The given function is $I\left(t\right)=0.8{e}^{-3t}\mathrm{sin}10t$.

Step 2: Calculation.

Consider the given information.

Substitute 0.1 for $t$ in the given function.

$I\left(0.1\right)=0.8{e}^{-3\left(0.1\right)}\mathrm{sin}10\left(0.1\right)\phantom{\rule{0ex}{0ex}}=0.8{e}^{-0.3}\mathrm{sin}1\phantom{\rule{0ex}{0ex}}=\text{0.49870}$

Substitute 0.5 for $t$ in the given function.

$I\left(0.5\right)=0.8{e}^{-3\left(0.5\right)}\mathrm{sin}10\left(0.5\right)\phantom{\rule{0ex}{0ex}}=0.8{e}^{-1.3}\mathrm{sin}5\phantom{\rule{0ex}{0ex}}=-0.20906$