Answer:
The answer is the third
S = 16 t²
Step-by-step explanation:
* Lets study the order pairs in C to find what is the relation
between the input (t) and the output (S)
∵ C = {(t , S): (0 , 0) , (1 , 16) , (2 , 64) , (3 , 144) , .............}
∵ (0 , 0) is the first point
∴ There is no plus or minus in the relation between S and t
∴ We refused the last answer S = 16(t + 1)² because
if t = 0 then S = 16(0 + 1) = 16 ≠ 0
- If we chose the first answer:
∵ S = 16t
∵ t = 0 ⇒ S = 16(0) = 0 ⇒ its right
∵ t = 1 ⇒ S = 16(1) = 16 ⇒ its right
∵ t = 2 ⇒ S = 16(2) = 32 ⇒ its wrong
∴ We refused the first answer
- If we chose the second answer:
∵ S = (16t)²
∵ t = 0 ⇒ S = (16×0)² = 0 ⇒ its right
∵ t = 1 ⇒ S = (16×1)² = 256 ⇒ wrong
∴ We refused the second answer
- If we chose the third answer:
∵ S = 16 t²
∵ t = 0 ⇒ S = (16)(0)² = 0 ⇒ its right
∵ t = 1 ⇒ S = (16)(1)² = 16 ⇒ its right
∵ t = 2 ⇒ S = (16)(2)² = 16 × 4 = 64 ⇒ its right
∵ t = 3 ⇒ S = (16)(3)² = 16 × 9 = 144 ⇒ its right
∴ every time we multiply 16 by the square of the value of t
∴ We accept the third answer
