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Chess asked in Science & MathematicsMathematics · 1 decade ago

Volume/Integral Calculus Question?

The volume of a cell increases at a rate of 100/(1 + t)^2 cubic micrometres/s. If the cell is initially 500 cubic micrometres in volume, find its ultimate size after a long period of time.

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  • rozeta53
    Lv 6
    1 decade ago
    Favorite Answer

    dV/dt=100/(1 + t)^2

    dV=100*dt/(1 + t)^2

    V(t)=∫100*dt/(1 + t)^2=-100/(1+t)+C

    t=0 ==> V(0)=500=-100+C ==> C=600

    V(t)=600-100/(1+t)

    t=∞ ==> V(∞)=600 cubic micrometres

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