Answer
(a)$v(0)=0$.
(b)
$v(5)\approx113.78ft/s$
$v(10)\approx155.64ft/s$
(c) See the image below.
(d) The terminal velocity of the diver is $180ft/s$
Work Step by Step
So, we have a function of velocity $v(t)$ in a given time $t$:
$v(t)=180(1-e^{-0.2t})$
(a) Initial velocity is the velocity at $t=0$
$v(0)=180(1-e^{-0.2\times0})=180(1-e^0)=180(1-1)=180\times0=0$
Which is logical, because at $t=0$ the sky diver hasn't started a motion yet, so the velocity is 0.
(b)
$t=5$
$v(5)=180(1-e^{-0.2\times5})=180(1-e^{-1})=180-\frac{180}{e})\approx113.78ft/s$
$t=10$
$v(10)=180(1-e^{-0.2\times10})=180(1-e^{-2})=180(1-\frac{1}{e^2})=180-\frac{180}{e^2}\approx155.64ft/s$
(c) We can graph the following function using a graphing calculator. See the image above.
(d) As we can clearly see from the graph the velocity $v(t)$ is approaching $180$ as $t$ gets bigger. So the terminal velocity of the diver is $180ft/s$