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Life cycle of butterfly is egg -> caterpillar -> butterfly.

Each week 5% of the eggs will hatch and 2% of the caterpillars will turn to butterflies.

You start with 100 eggs and 60 caterpillars.

Using calculus to obtain an equation which will refine your model for the amount of caterpillars at any time.

How many caterpillars are there after 40 weeks?