1. **State the problem:** We have a differential equation $y' = ky$ with initial condition $y(0) = 18$ and constant $k = \frac{3}{2}$. We want to find $y(23)$. 2. **Formula used:** The general solution to $y' = ky$ is $y(t) = y(0) e^{kt}$. 3. **Apply initial condition:** Given $y(0) = 18$, the solution becomes $y(t) = 18 e^{\frac{3}{2} t}$. 4. **Calculate $y(23)$:** Substitute $t = 23$: $$y(23) = 18 e^{\frac{3}{2} \times 23} = 18 e^{34.5}.$$ 5. **Interpretation:** The value $y(23)$ is $18$ times $e$ raised to the power $34.5$, which is a very large number. **Final answer:** $$y(23) = 18 e^{34.5}.$$