Step 1: Recall diode current equation.
For a diode:
\[
I = I_0 \left(e^{\frac{qV}{kT}} - 1\right)
\]
Step 2: Analyze forward bias condition.
In forward bias, voltage \( V \) is positive and large compared to \( kT/q \), so:
\[
I \approx I_0 e^{\frac{qV}{kT}}
\]
Step 3: Identify nature of relation.
Current increases exponentially with voltage.
Step 4: Graph behavior.
Initially current is small, then increases rapidly (exponential rise).
Step 5: Eliminate incorrect options.
Not linear, not parabolic, not sinusoidal.
Step 6: Confirm correct curve.
Hence, the graph is exponentially increasing.
Step 7: Final conclusion.
\[
\boxed{\text{Exponentially increasing curve}}
\]
Therefore, correct option:
\[
\boxed{(4)}
\]