Question

If $w=w_0{e}^{-kt}$, find the approximate value of $t$ when $w=7,w_0=50$, and $k=3.4$.

• A. $.52$
• B. $.54$
• C. $.56$
• D. $.58$
• E. $.60$

Answer 1

The correct option is D $.58$

Given,

$w=w_0{e}^{-kt}$

we have,

$w=7$

$w_0=50$

$k=3.4$

$t=?$

$7=50e^{-3.4\times t}$

$\frac{7}{50}=e^{-3.4t}$

$\ln \left(\frac{7}{50}\right)=-3.4t$

$t=-\frac{\ln \left(\frac{7}{50}\right)}{3.4}$

$\therefore t=0.578$