Answer
$2^{30}-1\approx 10^9 \text{ dollars}$
Work Step by Step
Each day Dwight receives twice as many dollars as the day before. In other words, his earnings form a geometric progression with $r=2$. On the first day he has 1 dollar. During 3$0$ days he earns
$$S_{30}=a_1\dfrac{1-r^{30}}{1-r}.$$
We substitute $a_1=1$ and $r=2$:
$$S=1\cdot \dfrac{1-2^{30}}{1-2}=\dfrac{2^{30}-1}{2-1}=2^{30}-1\approx 10^9 \text{ dollars!!!}$$
