Solve 16=0.05e^-lambdat

$$16 = 0.05 e ^ { - \lambda } t$$

Solve for t

$$t=320e^{\lambda }$$

Steps for Solving Linear Equation

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

$$0.05e^{-\lambda }t=16$$

The equation is in standard form.

$$\frac{1}{20e^{\lambda }}t=16$$

Divide both sides by 0.05e^{-\lambda }.

$$\frac{\frac{1}{20e^{\lambda }}t\times 20e^{\lambda }}{1}=\frac{16\times 20e^{\lambda }}{1}$$

Dividing by 0.05e^{-\lambda } undoes the multiplication by 0.05e^{-\lambda }.

$$t=\frac{16\times 20e^{\lambda }}{1}$$

Divide 16 by 0.05e^{-\lambda }.

$$t=320e^{\lambda }$$

Solve for λ

$$\lambda =\ln(t)-\ln(320)$$

$$t>0$$