Question

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

Answer 1

This equation is separable,

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

Integrate both sides and solve for
`A` :

`\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
`C` using the initial value.

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

Then the particular solution is

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