#1**+2 **

lets say x is year-2000. so you have (0, 10), (1, 26), (2, 70), (3, 144), (4, 247), and (5, 380).

to see if it is quadratic sequence, see if you can model it by y=ax^2+bx+c. obviously c=10, because of (0, 10), so now you have y=ax^2+bx+10.

next, a+b=16, by using (1, 26)

and finally, 4a+2b=60 by using (2, 70)

now you can find that a = 14 and b = 2, so you have the quadratic is y = 14x^2 + 2x + 10. this is a quadratic sequence, i am very confused....

you can still change it up and make a quadratic with huge coefficients by adding back the 2000 year i took away

for b),

here is a graph of y = 14x^2 + 2x + 10:

for c)

just find the first x when 14x^2 + 2x + 10 goes above 1000, and add 2000 to that.

first estimate and try 8.

14*64+16+10=840+56+16+10=896+16+10=922. super close, so try 9.

14*81 is already above 1000, so the first year is 2000+9 or 2009.

HOPE THIS HELPED!!!

asdf335 Jan 13, 2019