Find a solution to dA/dt=-6A if A(0)=6. A(t)=

Question

asked Apr 13, 2023 200k views

1 Answer

Rurp · Answer 1 · 2023-04-17T08:00:47+0000

This equation is separable,

$(dA)/(dt) = -6A \implies \frac{dA}A = -6\,dt$

Integrate both sides and solve for
:

$\displaystyle \int \frac{dA}A = -6 \int dt$

$\ln|A| = -6t + C$

$e^(\ln|A|) + e^(-6t+C)$

$\implies A(t) = Ce^(-6t)$

Solve for
using the initial value.

$A(0) = 6 \implies 6 = Ce^0 \implies C=6$

Then the particular solution is

$\boxed{A(t) = 6e^(-6t)}$