SME
Grade 9 Science · Biology
Disease and the immune system
Use this for “How much higher and how much sooner does the antibody level peak on a second exposure?”
Diagram
100
10
=
10
First peak 12 days after exposure; second peak 6 days after.
This is an example. Type your own values to start a new problem.
R
=
P₂
÷
P₁
d₁
Days to the first peak
example · days
d₂
Days to the second peak
example · days
s
Days sooner, second peak
worked out (not typed) · days
Formulas
R
=
P₂
P₁
10
=
100
10
s
=
d₁
−
d₂
6 = 12 − 6
Assumptions
•
Memory B and T cells left by a first exposure, or by a vaccine, answer a second exposure faster and stronger.
•
Antibody levels here are relative units, as on textbook graphs: only their ratio matters.
•
The second exposure comes on day 40, after the first response has faded.
Step-by-step
WE KNOW
P₁ = 10, P₂ = 100, d₁ = 12 days, d₂ = 6 days
FIND
times higher, second peak (R), days sooner, second peak (s)
Step 1 · Find times higher, second peak (R)
Use R = P₂ ÷ P₁
How many times the first peak fits into the second.
R
=
100
10
R
=
10
Step 2 · Find days sooner, second peak (s)
Use s = d₁ − d₂
The days the first response took, less the days the second took.
s
=
12
−
6
s
=
6
days
Check
Put the numbers back in. Both sides should match.
10
=
100
10
✓
6 = 12 − 6 ✓
Topic check
See what you know: 5 questions on this topic
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