Question

Work: Tetanus bacillus bacterium is cultured to produce tetanus toxin used in an inactive form for the tetanusvaccine. The amount of toxin produced per batch increases with time and then becomes unstable. The amount oftoxin (in grams) as a function of time t (in hours) can be approximated by: b(t) = -115zt2 + izt.

Answer 1

Solution

For this case we have the following equation:

$b(t)=-\frac{1}{1152}t^2+\frac{1}{12}t$

in order to find the time to get maximum we just need to find the vertex of the function so we have:

$t=-\frac{b}{2a}=-\frac{\frac{1}{12}}{-\frac{2}{1152}}=48$

Then the maximum amount is:

$b(48)=-\frac{1}{1152}(48)^2+\frac{1}{12}\cdot48=2$

Then the final answer is:

Maximum yield: 2

hours to produce the maximum yield: 48hr