suppose that another population of bacteria triples envy hour and starts with 400 bacteria. find an expression for the number n of bacteria after t hours and us

Question

suppose that another population of bacteria triples envy hour and starts with 400 bacteria. find an expression for the number n of bacteria after t hours and use it to estimate the rate of growth of the bacteria population after 2.5 hours. 

 

my first instinct was to do change in n over change in t which i got as (3,000-400)/(2.5-1)

 

idk if thats right but i don't really know what else to do

Answer 1

 

 

P(t) = 400*3^t

 

P(2.5) = 400*3^2.5 = 6235.383

 

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Numerically,

 

hour 0: 400

 

hour 1: 1200

 

hour 2: 3600

 

hour 3: 10800

 

Splitting the difference (10800 - 3600)/2 = 3600

Adding that to hour 2, 3600+3600 = 7200

which further supports the answer