Answer
$y=100e^{1.526x}$
Work Step by Step
Use Basic Logarithmic Properties: $b^{\log_{b}x}=x$,
replacing b with e and x with $(4.6)^{x}$
$y=100(4.6)^{x}$ is equivalent to $y=100e^{\ln(4.6)^{x}}$\qquad
... now, by the Power Rule: $\log_{\mathrm{b}}\mathrm{M}^{\mathrm{p}}=\mathrm{p}\log_{\mathrm{b}}\mathrm{M}$
$y=100e^{(\ln 4.6)x}$
Calculator:
$\ln 4.6\approx$1.5260563035 $\qquad$ ... round to 3 decimals
$\approx 1.526$,
$y=100e^{1.526x}$
