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.

Answer 1

20.00 thousand cell

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[(e^(0.18t))/(0.18)\right]_(0)^(3) \\ &=4+(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.