Worked example 1
The graph shows the concentration of a specific antibody in the blood following an initial vaccination at day 0 and a booster vaccination at day 28.
The primary response begins around day 5, peaks at 80 arbitrary units (AU) on day 14. After the booster at day 28, the antibody level is 20 AU. The secondary response begins almost immediately, reaching a peak concentration of 1200 AU on day 34.
Calculate the average rate of antibody production during the rapid phase of the secondary response, from day 28 to day 34. Give your answer in AU per day.
Show solution outline
- Identify the start and end points for the calculation:
- Start of the rapid secondary response phase: Day 28.
- End of the rapid phase (peak concentration): Day 34.
- Identify the antibody concentrations at these points:
- Concentration at day 28 = 20 AU.
- Concentration at day 34 = 1200 AU.
- Calculate the change in concentration and the time elapsed:
- Change in antibody concentration = Final concentration - Initial concentration
- Change = 1200 AU - 20 AU = 1180 AU.
- Time elapsed = 34 days - 28 days = 6 days.
- Calculate the rate:
- Rate = Change in concentration / Time elapsed
- Rate = 1180 AU / 6 days
- Rate = 196.67 AU per day.
- Final Answer: The average rate of antibody production during the secondary response is 197 AU per day (to 3 significant figures).