A cabbage plant carries 150 larvae when a spray of Bacillus thuringiensis begins…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A cabbage plant carries larvae when a spray of Bacillus thuringiensis begins. Each day of the larvae that are left die. The crop can bear larvae on a plant.
- How many larvae are on the plant after day?
- How many larvae are on the plant after days?
- After how many whole days are there fewer than larvae on the plant?
Need a reminder? The key ideaShow
Biocontrol uses living organisms. Ladybird: aphids. Dragonfly: mosquitoes. Bacillus thuringiensis: caterpillars, by the toxin that is released in the gut of the larva. Trichoderma: plant pathogens. Baculoviruses: insects, narrow spectrum. If a share of the larvae die each day, a number falls to after days. An average is the total divided by the number of plants.
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: larvae. Each day are left. Limit: .
Plan. Multiply by for each day.
Step 1. After 1 day. .
Step 2. After 3 days. .
Step 3. The limit. The numbers for days , and are , and . The count first falls below on day .
Answer: ; ; days.
Check. We can also solve . This gives , so the first whole day is .
Watch out. The count does not fall by of the start every day. Each day takes of what is left, so the fall slows down.
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