A virus is spreading such that the number of newly infected people increases by 8% a day. Initially 100 people were diagnosed with the virus. a. How many newly infected people will be in the 12th? b. How many days are needed to infect 3000 people?

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The virus is spreading such that the number of newly infected people increases by 8% a day. Initially 100 people were diagnosed with the virus.

In the 12th day, the number of newly infected people is `0.08*100*(1.08)^11 ~~ 18`

If the number of infected people is 3000 in D days, `3000 = 100*1.08^D`

=> `30 = 1.08^D`

=> `D = log 30/ log(1.08)`

=> `D ~~ 45`

In the 45th day there are 3000 infected people.

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