College Algebra (6th Edition)

$y=96e^{-0.968x}$
One of Basic Logarithmic Properties : $b^{\log_{b}x}=x$ Swap b with e and x with $(0.38)^{x}:$ $(0.38)^{x}=e^{\ln(0.38)^{x}}$ ...now apply The Power Rule: $\log_{\mathrm{b}}\mathrm{M}^{\mathrm{p}}=\mathrm{p}\log_{\mathrm{b}}\mathrm{M}$ $(0.38)^{x}=e^{\ln(0.38)^{x}}=e^{x\ln 0.38}$ So $y=96e^{x\ln 0.38}$ with $\ln 0.38\approx$-0.967584026262$\approx-0.968$ $y=96e^{-0.968x}$