Each piece is defined over some (limited) domain. When you are evaluating or graphing a piecewise function, you only evaluate or graph the function whose domain includes the variable value of interest.
Answer:Yes that is correct, 3(2t + d) is equal to 6t+3d. This is due to the distributive property of multiplication, or as I like to call it, the DPM. The DPM works for all multiplication and praentheses problems. For example, 7(2t+3d)=14t+21d. You multiply the coefficient of the whole parentheses by each number/variable in the equation. Another example is 5(n+s)=5n+5s.
1813 x

= 326.34
18% of 1813 people is 326.34 people
333 is a reasonable estimate.