In a simple teaching model, a person with HIV has 1000 helper T cells in each mm³ of blood, and the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a simple teaching model, a person with HIV has helper T cells in each mm³ of blood, and the count falls by each year.
- What is the count after year?
- What is the count after years, to the nearest whole number?
- After how many whole years is the count first below in each mm³?
Need a reminder? The key ideaShow
In allergy, IgE on mast cells makes the cells release histamine and serotonin. HIV is a retrovirus that destroys the helper T cells. A count below 200 helper T cells in each mm³ of blood is the sign of AIDS. In an ELISA plate a sample is positive when its reading is above the cutoff.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Start: per mm³. Each year the count is multiplied by .
Plan. After years the count is .
Step 1. One year. per mm³.
Step 2. Five years. per mm³.
Step 3. Below . After years the count is , which is still above . After years it is . So the first whole year below is year .
Answer: ; ; year .
Check. The exact time is years, so the count is below during the eighth year.
Watch out. This is a model. Real counts do not fall by the same share every year, and treatment stops the fall.
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