Question

A cell culture contains 6 thousand cells, and is growing at a rate of r ( t ) = 11 e 0.23 t r(t)=11e0.23t thousand cells per hour. find the total cell count after 3 hours. give your answer accurate to at least 2 decimal places.

Answer 1

Answer:10.32 thousand cells

Step-by-step explanation:

Given

6000 cells Growing at the rate of

$r(t)=11e^{0.23t}$

Therefore

$r=6+\int_{0}^{3}11e^{0.23t}dt$

Where r represent the total cells after t sec

$r=6+\left ( \frac{e^{0.23t}}{0.23}\right )_0^3$

$r=6+\left ( \frac{e^{0.23\times 3}-e^0}{0.23} \right )$

$r=6+\left ( \frac{1.993-1}{0.23} \right )=6+4.320$

$r=10.32 thousands\ cells\ will\ be\ there\ after\ 3\ hours$

Answer 2

The rate of growth of cultured cells is:
r(t)=11e^0.23t
number of Cells when:
t=1
r(t)=11e^0.23*1
r(t)=13.8446
number of cells will therefore be:
6000×13.8446
=83067.6

t=2
r(2)=11e^(0.23*2)
r(2)=17.425
number of cells
17.425×6000
=104,550

t=3
r(3)=11e^(0.23*3)
r(3)=21.931
number of cells
6000×21.931
=131,586
Thus the total number of after the 3rd hour will be:
104550+131586+83068
=319,204