# The initial size of a particular substance is 75. After 3 hours the substance count is 4500.6.Find a function n(t) = n,e" that models the population after t hours. Round your answer to fourа.decimal places.b.Find the population after 5 hours. Round to one decimal place.After how many hours will the number of bacteria reach 10,000? Give an exact AND an approximateanswer rounded to one decimal place.С.

Question
1 views help_outlineImage TranscriptioncloseThe initial size of a particular substance is 75. After 3 hours the substance count is 4500. 6. Find a function n(t) = n,e" that models the population after t hours. Round your answer to four а. decimal places. b. Find the population after 5 hours. Round to one decimal place. After how many hours will the number of bacteria reach 10,000? Give an exact AND an approximate answer rounded to one decimal place. С. fullscreen
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Step 1

We are given that the initial size of a particular substance is 75 and after 3 hours the substance count is 4500. help_outlineImage Transcriptionclose(a) We need to find a function n(t) = noert that models the population after t hours By the above information, no = 75 and when t 3 4500 = noe3r => 4500 = 75 x e3r => 40 = e3r =>In 40 3r Ine Taking "In" both sides) => 3.6889 = 3r =>r = 1.2296 So, the model of the population after t hours are n(t) = 75e1.2296t fullscreen
Step 2

Now,

... help_outlineImage Transcriptionclose(b) We need to find the population after 5 hours So, we have t 5, n(5) 75e1.2296 x5 =35083.56666 35083.6 (c) We need to find that after how many hours the number of bacteria reach 10,000. 10000 75e1.2296t So, 10000 e1.2296t 75 10000 In 1.2296t In e (Taking "In" both sides) => = 75 =>In(10000) - In(75) 1.2296t =>t = 3.97922 And the approximate answer rounded to one decimal place is t = 3.9. fullscreen

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