How do you compute for fc and t in modulating an I and Q component I know that in a $2^b$-ary QAM system you need to modulate the $I$ and $Q$ components through the mixer and are separated by 90° through a local oscillator (by applying a $\cos$ and $\sin$).

By mixing them through the mixer, the $I$ component will be multiplied by a $\cos(2\pi f_c t)$ and $Q$ by $\sin(2\pi f_c t)$. My question is, if I have a 8 bit sampler and the sampling frequency I used is 10 kHz, what will be my value for the carrier frequency $f_c$ and the time sweep, $t$? 

My idea is that I can compute the carrier frequency by computing for the symbol rate (bit rate over the number of symbols) and multiplying it by 2 to satisfy the Nyquist Sampling rate. Is that true? And I really don't have any idea what increment value of $t$ I will use.
The answer is: it depends on the pulse shape.

A 16-QAM baseband signal can be written as $$s_{BB}=\sum_{k=0}^{N-1} a_k p(t-kT_p),$$ where $a_k$ is a complex symbol taken from your 16-QAM constellation, $R_p=1/T_p$ is the pulse rate (how many pulses per second you transmit), and $p(t)$ is the pulse shape (ideally, $p(t)$ is a Nyquist pulse).

The bandwidth of $s_{BB}(t)$ is the same as the bandwidth of $p(t)$ (assuming you're transmitting uncorrelated data). Assume this bandwidth is $B$. Then, after mixing with the carrier, the passband signal's maximum frequency is $f_c+B$, and you need a sampling frequency $f_s&gt;2(f_c+B)$ to satisfy Nyquist.

If you don't know what the pulse shape is, then you're probably transmitting rectangular, non-overlapping pulses. As a rule of thumb, I define the bandwidth of a rectangular pulse as five times the pulse rate: $B=5R_p$. Note that many textbook authors, such as Stallings, use $B=R_p$. I prefer to be conservative and define a larger bandwidth.

Then, your sampling frequency is $f_s&gt;2(f_c+5R_p)$.

As an example, let's say that you want to transmit 1000 pulses per second, with a carrier frequency of 1 MHz, and rectangular pulses. Then,

fs = 2*(1e6+5*1000);  % or larger
t = 0:1/fs:Tend       % Tend depends on how many pulses you transmit