So the velocity function is defined as $v(t) = Ce^{kt} + \frac{9.8}{k}$. It is given that when t = 0, velocity = 0. This leads me to this relationship between C and k: $0 = C + \frac{9.8}{k}$
Now, if the limit to infinity of the velocity function is -35
$\lim_{t \to \infty} v(t) = -35$ How would I find what C and k are? What I have tried is as follows:
$ \lim_{t \to \infty} Ce^{kt} + \frac{9.8}{k} = -35$
Substituting the fraction by the above relationship between C and k gives:
$ \lim_{t \to \infty} Ce^{kt} - C = -35$
But now...
$ \lim_{t \to \infty} C(e^{kt} - 1) = -35$
Dividing by $e^{kt} $ gives 0 multiplied by C
$ \lim_{t \to \infty} C(e^{kt} - 1) = -35$
$ \lim_{t \to \infty} C(1 - \frac{1}{e^{kt}}) = -35$
$ \lim_{t \to \infty} C(1 - 0) = -35$
$ \lim_{t \to \infty} C = -35$
However, upon subsequently working out k as 0.28 graphing this, this is wrong.The signs should be switched around where C = 35 and k = -0.28. Is anyone able to tell me how I went wrong? Moreover, is this THE best way to evaluate limits to infinity in this way.
Thanks!