Question

what is the rule of the input output table input 2 output 11 input 3 output 15 input 5 output 18 input 8 output? what is the rule?

Answer 1

2 --> 11
3 --> 15
5 --> 18
8 --> ??

slopes are different, so , not linear
assume it is quadratic
y = ax^2 + bx + c

11 = 4a+2b+c
15= 9a+3a+c
18 = 25a+5b+c

#2 - #1 ---> 5a + b = 4
#3 - #2 ---> 16a + 2b = 3

16a + 2b = 3
10a + 2b = 8
subtract
6a = -5
a = -5/6
then 5(-5/6) + b = 4
-25 + 6b = 24
6b = 49
b = 49/6

in 4a+2b+c=11
4(-5/6) + 2(49/6) + c = 11
-20 + 98 + 6c = 66
6c = -12
c = -2

<b>y = (-5/6)x + (49/6)x-2</b>

so if input = x = 8
y = output = (5/6)(8) + (49/6)(8) - 2
= 70

check:
if input is 2, output = (-5/6)(2) + (49/6)(2) - 2 = 11
if input is 3, out put = (-5/6)(9) + (49/6)(3) - 2 = 15
if input is 5, out put is (-5/6)(25) + (49/6)(5) - 2 = 18
All is good !

Answer 2

eqution is y=2exponet(x)+2 input value if y =34