1. **State the problem:** We are given the amount of mold on a fruit at different times and need to find the initial amount of mold (at time 0 seconds). 2. **Identify the pattern:** The mold amounts are 24, 96, 384, and 1536 at times 2, 4, 6, and 8 seconds respectively. 3. **Check if the growth is exponential:** Calculate the ratio between consecutive amounts: $$\frac{96}{24} = 4, \quad \frac{384}{96} = 4, \quad \frac{1536}{384} = 4$$ The amount of mold quadruples every 2 seconds. 4. **Write the exponential growth formula:** $$M(t) = M_0 \times r^{\frac{t}{T}}$$ where $M(t)$ is the mold at time $t$, $M_0$ is the initial amount, $r$ is the growth factor per interval $T$. 5. **Plug in known values:** Here, $r=4$, $T=2$ seconds, and at $t=2$ seconds, $M(2) = 24$. 6. **Solve for $M_0$:** $$24 = M_0 \times 4^{\frac{2}{2}} = M_0 \times 4^1 = 4 M_0$$ Divide both sides by 4: $$\frac{24}{\cancel{4}} = M_0 \times \cancel{4} \Rightarrow 6 = M_0$$ 7. **Interpretation:** The initial amount of mold was 6 mm². **Final answer:** B. 6 mm²