Answer :
ANSWER
D. d = 5.25t²
EXPLANATION
To find which of these equations represents the relationship mentioned, we can try a few values, replacing t and checking if the result is the corresponding value of d that appears on the table.
If we try the second pair, t = 2 and d = 21 in the first option,
[tex]d=10.5\cdot2^2=10.5\cdot4=42[/tex]Not true, because the result is not d = 21.
The equation of the second option is similar, but the exponent of t is 3 instead of 2, so the number will be even greater than 42. Because of this, we can conclude that option B is not correct either.
The equation of option C is a linear equation, but,
[tex]d=5.25\cdot2=10.5[/tex]Therefore, option C is not correct.
Finally, it seems like the answer is option D,
[tex]d=5.25\cdot2^2=5.25\cdot4=21[/tex]If we try the other values in the table, we will find that this equation is satisfied by all of them.
Hence, the equation that represents the relationship between t and d, is d = 5.25t².