Question

Calculate G(17), where dG/dt = t^−1/2 and G(3) = −3. (Round your answer to two decimal places.) G(17)=?

Answer 1

`G(17) \approx 1.782`

Explanation:

Let
`(dG)/(dt) = t^(-1/2)` and
`G(3) = -3`, we proceed to find
`G(t)` by integrating
`(dG)/(dt)` in time:

`G(t) = \int {t^(-1/2)} \, dt`

`G(t) = (t^(1/2))/((1)/(2) ) + C`

`G(t) = 2\cdot t^(1/2) + C` (1)

Where
`C` is the constant of integration. If we know that
`t = 3` and
`G(3) = -3`, then the constant of integration:

`-3 = 2\cdot 3^(1/2) + C`

`C = -6.464`

The resultant function is
`G(t) = 2\cdot t^(1/2) -6.464`.

Lastly, we evaluate this function at
`t = 17`:

`G(17) = 2\cdot 17^(1/2)-6.464`

`G(17) \approx 1.782`