Can someone show me, step-by-step, how to solve this equation?
Solve for d.
N(t)=20 000 x 2^(t/d), where t=25
So, N(25)= 20 000 x 2^(25/d)
Thanks.
Are you given what N(25) is? If not,
$\displaystyle \begin{aligned}
N(25) &= 20 000 \times 2^{(25/d)} \\
\frac{N(25)}{20000} &= 2^{(25/d)} \\
\ln \left(\frac{N(25)}{20000}\right) &= \ln (2^{(25/d)}) \\
\ln \left(\frac{N(25)}{20000}\right) &= \frac{25}{d} \cdot \ln 2 \\
\frac{\ln \left(\frac{N(25)}{20000}\right)}{\ln 2} &= \frac{25}{d}
\end{aligned}$
$\displaystyle \begin{aligned}
\frac{\ln 2}{\ln \left(\frac{N(25)}{20000}\right)} &= \frac{d}{25} \\
d &= \frac{25\ln 2}{\ln (N(25)) - \ln 20000}
\end{aligned}$
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