In a model, the number of mosquitoes in a colony is multiplied by 5 each week if nothing is done…
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 model, the number of mosquitoes in a colony is multiplied by each week if nothing is done. Weekly cleaning removes a share of the breeding sites, so the weekly factor becomes .
- What is the weekly factor when of the sites are cleaned?
- A colony starts with mosquitoes, and of the sites are cleaned each week. How many mosquitoes are there after weeks?
- What least share of the sites must be cleaned to stop the growth?
Need a reminder? The key ideaShow
Amoebiasis is caused by a protozoan, ascariasis by a roundworm, filariasis by a filarial worm and ringworm by fungi. Prevention is by personal hygiene, public hygiene, control of vectors and vaccination. A population grows by a fixed factor each week, and cleaning removes a share of the sites.
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. Growth factor with no control: . Weekly factor: .
Plan. Work out the factor, then multiply the start by the factor once each week. For the least share, set the factor to .
Step 1. cleaned. .
Step 2. cleaned. The factor is . After weeks: mosquitoes.
Step 3. The least share. gives , so , which is .
Answer: ; mosquitoes; .
Check. At the number stays at for ever in this model. At any lower share it grows.
Watch out. This is a teaching model. It shows why a half hearted clean up is not enough, but real numbers vary with the weather and the species.
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