Answer
$y=0.75e^{0.3794t}$
Work Step by Step
$(0, \frac{3}{4})$ lies on the curve.
Thus, $$\frac{3}{4} = Ce^{k.0}$$
Or, $$C=\frac{3}{4}=0.75$$
$(5, 5)$ lies on the curve.
Thus, $$5 = 0.75e^{5k}$$
Or, $$e^{5k}=\frac{20}{3}$$ $$k = \frac{\ln(20/3)}{5} = 0.3794$$
So, the function is $$y=0.75e^{0.3794t}$$
