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.

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