This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.(a) Find an exponential modeln(t) = n02t/afor the number of bacteria in the culture after t hours. n(t) =(b) Estimate the number of bacteria after 26 hours. (Round your answer to the nearest whole number.)bacteria(c) After how many hours will the bacteria count reach 10,000? (Round your answer to one decimal place.)

(a)

(b)1,482,833

(c)15.2 hours

Step-by-step explanation:

where is the initial population, t=time(in hours),

a=interval of growth doubling

(a) =8, a=1.5 hours

After t hours, the number of bacteria in the culture

(b)The number of bacteria after 26 hours

After 26 hours, the number of bacteria in the culture will be approximately 1,482,833.

(c)If n(t)=10,000, we want to determine the value of t.

Taking the natural logarithm of both sides

=15.2 hours (correct to 1 decimal place)

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step-by-step explanation: