Answer:
1. The constraints for the variable t using set builder notation are as follows:
t ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
This means that t is a variable that can take on values from 0 to 9, inclusive. These values correspond to the number of years since 1999, which is the time period covered by the function.
2. To determine the value of s(7), we need to substitute 7 for t in the function s(t) and solve for s. The function s(t) is given by s(t)=1.084x+17.392, so substituting 7 for t gives us s(7)=1.084*7+17.392=24.98. Therefore, the value of s(7) is 24.98 billions of dollars.
3. In context, the value of s(7) represents the amount of money the United States government spent on science and technology 7 years after 1999. This value can be interpreted as the amount of money spent in 2006.
The key feature that is found when solving s(t)=0 is the y-intercept of the graph of s(t)=1.084x+17.392. The y-intercept is the point at which the graph of the function crosses the y-axis. On the graph of s(t)=1.084x+17.392, the y-intercept is the point (0,17.392).
4. The value for s(t)=0 is not reasonable in the context of this problem, because it would represent the amount of money the United States government spent on science and technology in 1999, which is the beginning of the time period covered by the function. However, the y-intercept of the graph of s(t)=1.084x+17.392 is 17.392, which is not equal to 0. This suggests that the government was already spending some amount of money on science and technology in 1999, which is a more reasonable assumption.