A cell culture currently contains 4 thousand cells, and is growing at a rate of r (t) = 8e^0.18t thousand cells per hour, where t is the num

Question

A cell culture currently contains 4 thousand cells, and is growing at a rate of r (t) = 8e^0.18t thousand cells per hour, where t is the number of hours since now. Find the total cell count after 3 hours. Give your answer accurate to at least 2 decimal places.

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Thái Dương 1 day 2021-07-21T05:12:42+00:00 1 Answers 0 views 0

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    2021-07-21T05:14:40+00:00

    Answer:

    20.00 thousand cell

    Step-by-step explanation:

    The problem can be solved using integration

    \begin{aligned} r &=4+\int_{0}^{3} 8 e^{0.18 t} d t \\ &=4+3 \cdot\left[\frac{e^{0.18t}}{0.18}\right]_{0}^{3} \\ &=4+\frac{3}{0.18}\left(e^{0.18(3)}-e^{0.18(0)}\right) \\ &=19.9996 \end{aligned}

    \approx 20.00 thousand cells

    the correct answer upto 2 decimal place.

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