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Create a table to find the second differences for the polynomial 36 − 16t^2 for integer values of t...
4 months ago
Q:
Create a table to find the second differences for the polynomial 36 − 16t^2 for integer values of t from 0 to 5.
Accepted Solution
A:
Step-by-step explanation:[tex]f(t)=36-16t^2[/tex]at t = 0[tex]y=36[/tex]at t = 1[tex]f(1)=36-16\times 1^2\\\Rightarrow f(1)=20[/tex]at t = 2[tex]f(2)=36-16\times 2^2\\\Rightarrow f(2)=-28[/tex]at t = 3[tex]f(3)=36-16\times 3^2\\\Rightarrow f(3)=-108[/tex]at t = 4[tex]f(4)=36-16\times 4^2\\\Rightarrow f(4)=-220[/tex]at t = 5[tex]f(4)=36-16\times 5^2\\\Rightarrow f(5)=-364[/tex]First difference[tex]f(1)'=f(1)-f(0)=20-36=-14[/tex][tex]f(2)'=f(2)-f(1)=-28-20=-48[/tex][tex]f(3)'=f(3)-f(2)=-108--28=-80[/tex][tex]f(4)'=f(4)-f(3)=-220--108=-112[/tex][tex]f(5)'=f(5)-f(4)=-364--220=-144[/tex]Second difference[tex]f(2)'-f(1)'=-48--14=-34[/tex][tex]f(3)'-f(2)'=-80--48=-32[/tex][tex]f(4)'-f(3)'=-112--80=-32[/tex][tex]f(5)'-f(4)'=-144--112=-32[/tex]0 20 -28 -108 -220 -364 -14 -48 -80 -112 -144 -34 -32 -32 -32