Question

I’m not sure how to figure out what numbers to fill in and the equation

Answer 1

Lets calculate linear equation
assume
y = f(x)= mx +b

now given
f(0) = 2
m×0+b = 2
b = 2
so b = 2
given f(4) = 0.125 = 1/8
m×4 + 2 = 1/8
4m = 1/8-2= -15/8
m = -15 /(8×4) = -15/32

so linear equation is
y = mx + b = -15x/32 + 2


exponential equation is same as you have written

y = 2(0.5)^x

now put values of x in each equation to get value of y

x =0

linear y = -15×0/32+2 = 2

exp y = 2(0.5)^0 = 2×1 = 2

x =1

linear y = -15×1/32+2 = 2-15/32= 49/32

exp y = 2(0.5)^1 = 2×1/2 = 1

x =2

linear y = -15×2/32+2 = 2-30/32= 17/16

exp y = 2(0.5)^2 = 2×1/4 = 0.5

x =3

linear y = -15×3/32+2 = 2-45/32= 19/32

exp y = 2(0.5)^3 = 2×1/8= 0.25

x =4

linear y = -15×4/32+2 = 2-60/32= 4/32 = 0.125

exp y = 2(0.5)^4= 2×1/16 = 1/8= 0.125