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.

Respuesta :

Answer:

20.00 thousand cell

Step-by-step explanation:

The problem can be solved using integration

[tex]\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}[/tex]

[tex]\approx 20.00[/tex] thousand cells

the correct answer upto 2 decimal place.