A gardener develops an eco-friendly spray that will kill harmful insects on fruit trees without contaminating the fruit. A trial is to be conducted with 100 000 insects. The gardener expects the spray to kill 35% of the insects each day and that exactly 5000 new insects will be produced each day.

The number of insects expected at the end of the th day of the trial is

1. Show that  .  (2 marks)
   

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2. Show that  .  (1 mark)
   

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3. Find the expected insect population at the end of the fourteenth day, correct to the nearest 100.  (1 mark)
   

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