The expression for the constant c with no negative exponent is expressed as [tex]c=\dfrac{B^t(k-P)}{P}[/tex]
The subject of the formula is a way of representing a variable in terms of other variables in a given equation.
Given the expression:
[tex]P=\dfrac{k}{1+cB^{-t}}[/tex]
We are to make the constant c the subject of the formula as shown:
Cross multiply
[tex]P(1+cB^{-t})=k\\[/tex]
Expand the bracket
[tex]P+PcB^{-t}=k\\PcB^{-t}=k-P\\cPB^{-t}=k-P[/tex]
Divide both sides by [tex]PB^{-t}[/tex]
[tex]\dfrac{cPB^{-t}}{PB^{-t}}= \dfrac{k-P}{PB^{-t}} \\\dfrac{c}{1} = \dfrac{k-P}{PB^{-t}} \\c= \dfrac{k-P}{PB^{-t}}\\[/tex]
Since [tex]B^{-t}=\frac{1}{B^t}\\[/tex]
The expression becomes:
[tex]c= \dfrac{k-P}{P*\frac{1}{B^t} }\\c= \dfrac{k-P}{\frac{P}{B^t} }\\c=\dfrac{B^t(k-P)}{P}[/tex]
Hence the expression for the constant c is expressed as [tex]c=\dfrac{B^t(k-P)}{P}[/tex]
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