Question

For the first 10 days in December, a plant cell grew in such a way that t days after Dec. 1, the volume oof the cell was increasing at a rate of (12-t)^-2 cubic micrometers/day.If on Dec. 3, the volume of the cell was 3 cubic micrometer, what was the volume on Dec. 8?

Answer 1

we have
dv/dt = 1/(12-t)^2
so, v(t) = 1/(12-t) + C
v(2) = 3, so
1/(12-2) + C = 3
C = 29/10
v(t) = 1/(12-t) + 29/10
Now you can find v(7)