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B(t)

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AP Calculus AB/BC

Definition

The function B(t) represents the number of births in the colony as a function of time. In this case, it is modeled by the square root of t.

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Practice Questions (1)

You have developed a new strain of bacteria in your lab. You have made DNA modifications that allow it to become resistant to an antibiotic. However, a side effect of the antibiotic is the inability to reproduce as quickly as the original strain. You find that the number of births in the colony as a function of time is B(t) = √t. Additionally, you find that the number of deaths in the colony as a function of time can be modeled by the parametric function D(t) = ln(t). Find the value of the parametric second derivative, d^2B/dD^2, at time t = 2.

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