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.

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Asked Oct 23, 2019
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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 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.
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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 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.

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Expert Answer

Step 1

We are given that the initial size of a particular substance is 75 and after 3 hours the substance count is 4500.

(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
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(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

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Step 2

Now,

...
(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.
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(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.

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Tagged in

Math

Calculus

Functions