A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t. Use either fractions, or decimals rounded to 4 places

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A population of bacteria is initially 6000. After three hours the population is 3000.   If this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t.   Use either fractions, or decimals rounded to 4 places

Arnold Odonnell · Accepted Answer

Step 1  Given, A population of bacteria is initially 6000. After three hours the population is 3000.  We know that, the exponential function is given as  P=P0ert  where P0 is the initial value  r is the rate  P is the total value  t is time  Step 2  Now, Initial value, P0=6000  P=3000  t=3  The exponential function becomes  3000=6000e3r  ⇒12=e3r  using ln on both sides,  ⇒ln⁡(0.5)=ln⁡(e3r)  ⇒ln⁡(0.5)=3rlog⁡(e)  ⇒ln⁡(0.5)=3r  ⇒ln⁡(0.5)3=r  ⇒r=−0.2310  The exponential function that represents the size of the bacteria population after t hours.  is given as  P=6000e−.2310t

A population of bacteria is initially 6000. After three hours the population is

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