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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.

$I\left(0.5\right)=0.8{e}^{-3\left(0.5\right)}\mathrm{sin}10\left(0.5\right)\phantom{\rule{0ex}{0ex}}=0.8{e}^{-1.3}\mathrm{sin}5\phantom{\rule{0ex}{0ex}}=-0.20906$ ### Want to see more solutions like these? 