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January 25, 2015

January 25, 2015

Posted by **Sara** on Tuesday, November 30, 2010 at 6:29pm.

- Calculus -
**MathMate**, Tuesday, November 30, 2010 at 7:16pmGiven

A(t)=20(1/2)^(t/140)

We look for A'(t)

Use implicit differentiation.

Take ln on both sides

ln(A)=ln 20 + (t/140)ln(1/2)

differentiate with respect to t

(1/A)dA/dt = 0 + ln(1/2)/140

substitute A

dA/dt = ln(1/2)/140*20(1/2)^(t/140)

substitute -ln(2) for ln(1/2)

dA/dt = -(ln(2)/7)*(1/2)^(t/140)

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