P30 - Suppose a drug is administered that affects 80 of the...

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Project 30 MAC 2233 1. Suppose that the number of worldwide users of a certain internet service is growing expo- nentially. Suppose that, after assessing the data, there were 100 million users originally, and 140 million users at the end of the second year. a) Write a formula for the number of users N (in millions) at the end of t years. b) How many users will there be after 5 years? c) After how many years will there be one billion users (1000 million)? 2. Drug therapy can be a hardship for patients with a tumor, so once administered, one would only like to reapply treatment after the tumor has again begun to grow. Suppose that the number of cancerous cells in a tumor is the constant N ; for simplicity, take N = 1000
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Unformatted text preview: . Suppose a drug is administered that affects 80% of the 1000 cancerous cells, and they begin to decay exponentially, so that 1 4 of affected cells remain after one week. Write a formula A for the number of these cells that remain after t weeks. Suppose the other 20% of the 1000 cancerous cells are unaffected, and continue to grow expo-nentially, so that they double in number after 2 weeks. Write a formula U for the number of these unaffected cells that remain after t weeks. The total number of cancerous cells after t weeks is A + U . Show that the tumor is at its minimum relative size after 1.6 weeks. (To ﬁnd the critical number, note that if Ae x = Be y , then A B = e y-x )...
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