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[answered] A bacteria culture is started with 200 bacteria. After 2 ho


?A bacteria culture is started with 200 bacteria. After 2 hours, the population has grown to 290 bacteria. Suppose the population grows exponentially. Answer the following questions: a.) Write the recursive formula for Pn. b.) Find P1 and P2. c.) Write the explicit formula for Pn d.) Use the formula for part c ?to predict the number of bacteria after 8 hours. Round to the nearest bacteria.


n Pn 1 r P0

 

2 P2 1 r P0

 

2 290 1 r 200

 

290

 

2 1 r 200

 

290 1 r

 

200

 

290 1 0.20416

 

200 r a)

 

Pn 1 r Pn 1

 

Pn 1 0.20416 Pn 1

 

Pn 1.20416 Pn 1 b)

 

P1 1.20416 P0 1.20416 200 240.832 241

 

P2 1.20416 P1 1.20416...

 


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