Answer
The function $y=4e^{\frac{2}{3}x}$ matches with the graph labeled (b)
Work Step by Step
y-axis intercept ($x=0)$:
$y=4e^{\frac{2(0)}{3}}=4e^0=4$
The graph of $y=ae^{bx}$ increases as $x$ increases when $b\gt0$. In this case $b=\frac{2}{3}$.