Rate of a chemical reaction

Text

In a reaction the amount of product formed after $t$ minutes is $x(t)=20t-2t^{2}$ grams. Find the reaction rate (in g/min) after $2$, $5$ and $6$ minutes and comment on the sign.

Solution

Reaction rate: $x'(t)=20-4t$.

• $x'(2)=12\text{ g/min}$;
• $x'(5)=0\text{ g/min}$ (peak amount reached);
• $x'(6)=-4\text{ g/min}$: negative, the product starts to decompose. $\boxed{x'(2)=12;\quad x'(5)=0;\quad x'(6)=-4\ \text{(g/min)}}$