Dr. Silas studies a culture of bacteria under a microscope. The function b2(t)=1200(1.8) represents the number of bacteria t hours after Dr. Silas begins her study. (a) What does the value 1200 represent in this situation?

(b) What does the value 1.8 represent in this situation?

(c) The number of bacteria in a second study is modeled by the function b2(t)=1000(1.8)t .
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?

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  a) the number of bacteria at the start of the study

  b) the growth factor each hour

  c) the number of bacteria at the start of the study

  d) the first study started with 200 more bacteria

Step-by-step explanation:

When you have an exponential equation of the form ...

  f(t) = a×g^t

you note that f(0) = a. That is, 'a' is the "initial value" or "y-intercept".

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(a) In the equation ...

  b2(t) = 1200·1.8^t

the value 1200 is the initial value, b2(0), the value when t=0. The variable 't' is the number of hours since the study began, so t=0 represents the start of the study.

The value 1200 is the number of bacteria at the start of the study.

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(b) Each time t increases by 1 units, an additional factor of 1.8 multiplies the bacteria count. Thus, 1.8 is the "growth factor" each hour.

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(c) As in part (a), the multiplying constant in the exponential equation is the initial value. Here, 1000 represents the number of bacteria at the start of the second study.

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(d) The difference between 1200 and 1000 is the difference between the numbers of bacteria at the start of the two studies.

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step-by-step explanation: