Subjects calculus

Rate Change 2A3203

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem statement:** We need to find the average mass of the compound remaining over the interval $0 \leq t \leq 25$ using integration. 2. **Recall the formula for average value of a function:** The average value $\bar{M}$ of a function $M(t)$ over the interval $[a,b]$ is given by $$\bar{M} = \frac{1}{b-a} \int_a^b M(t) \, dt$$ 3. **Apply the formula:** Here, $a=0$ and $b=25$, so $$\bar{M} = \frac{1}{25-0} \int_0^{25} M(t) \, dt = \frac{1}{25} \int_0^{25} M(t) \, dt$$ 4. **Evaluate the integral:** To proceed, we need the explicit function $M(t)$ representing the mass remaining. Since it is not provided in the question, we cannot compute the integral directly. 5. **Conclusion:** If you provide the function $M(t)$, I can help compute the integral and find the average mass to two decimal places. Since the first question in the message is (i) about finding the rate of change $M'(t)$, I will solve that first as per instructions.