The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1000. Find the doubling period.    Find the population after 90 minutes.    When will the population reach 14000?

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter10: Exponential And Logarithmic Functions
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Problem 445RE: Mouse populations can double in 8 months (A=2A0) . How long will it take for a mouse population to...
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The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1000.

Find the doubling period.   

Find the population after 90 minutes.   

When will the population reach 14000? 

Expert Solution
Step 1

Given 

Initially the count in a bacteria culture = 300

after 35 minutes the population had increased to 1000.

Step 2

Assume the exponential growth for bacteria, 

Exponential growth model 

A(t)=A0ekt                 ........(1)

Where 

A0=initial count of bacteria

k=growth constant 

 

From the given information 

After 35 minutes the population had increased to 1000.

A(t)=A0ekt1000=300ektekt=1000300ekt=103Take natural log on both sides lnek35=ln10335k=ln103k=ln10335

Now the equation (1) becomes 

A(t)=300eln10335t                           (2)

Step 3

a) Find the doubling period.   

Here 

A(t)=2×300=600

 

From the equation (2)

A(t)=300eln10335t600=300eln10335teln10335t=600300eln10335t=2Take natural log on both sideslneln10335t=ln2ln10335t=ln2t=35×ln2ln103t=20.15 minutes

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