The variables $x$ and $y$ are connected by the equation $y = \frac{k}{b^x}$, where $k$

Question

The variables $x$ and $y$ are connected by the equation $y = \frac{k}{b^x}$, where $k$ and $b$ are constants. The straight line passes through the points $(0, 1)$ and $(5, 17)$ obtained by plotting $\ln y$ against $x$. Find the values of $k$ and $b$. Find the value of $y$ when $x = 0.5$.

Accepted Answer

(a) $k=e$, $\displaystyle b=e^{-16/5}$ (b) $y=13.5\text{ (3 s.f.)}$

Linear Law

Linear Law

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