Solve 2500=A*e^4.17k

$$2500 = A \cdot e ^ { 4.17 k }$$

Solve for A

$$A=2500e^{-\frac{417k}{100}}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$Ae^{4.17k}=2500$$

The equation is in standard form.

$$e^{\frac{417k}{100}}A=2500$$

Divide both sides by e^{4.17k}.

$$\frac{e^{\frac{417k}{100}}A}{e^{\frac{417k}{100}}}=\frac{2500}{e^{\frac{417k}{100}}}$$

Dividing by e^{4.17k} undoes the multiplication by e^{4.17k}.

$$A=\frac{2500}{e^{\frac{417k}{100}}}$$

Divide 2500 by e^{4.17k}.

$$A=2500e^{-\frac{417k}{100}}$$

Solve for k

$$k=\frac{-100\ln(A)+200\ln(50)}{417}$$

$$A>0$$