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Math Help - Solving for d

  1. #1
    Junior Member
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    Solving for d

    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.
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  2. #2
    Super Member
    Joined
    May 2009
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    Quote Originally Posted by oryxncrake View Post
    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,

    \begin{aligned}<br />
N(25) &= 20 000 \times 2^{(25/d)} \\<br />
\frac{N(25)}{20000} &= 2^{(25/d)} \\<br />
\ln \left(\frac{N(25)}{20000}\right) &= \ln (2^{(25/d)}) \\<br />
\ln \left(\frac{N(25)}{20000}\right) &= \frac{25}{d} \cdot \ln 2 \\<br />
\frac{\ln \left(\frac{N(25)}{20000}\right)}{\ln 2} &= \frac{25}{d}<br />
\end{aligned}
    \begin{aligned}<br />
\frac{\ln 2}{\ln \left(\frac{N(25)}{20000}\right)} &= \frac{d}{25} \\<br />
d &= \frac{25\ln 2}{\ln (N(25)) - \ln 20000}<br />
\end{aligned}


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