Linear or an exponential function

Question

x |-4|-2|0|2|4

y |0.0128|0.32|8|200|500

f(x)=

Answer 1

y=ab^x

8=ab^0=a

y=8b^x

200=8b^2

b^2=200/8= 25

b=5

y=

f(x) =8(5^x) is the exponential equation

check the last point (4,500)

500=8(5^4)= 8(625)

check 2nd point

(-2,.32)

.32=8(5^-2)= 8(1/25)=32/100

check 1st point

(-4,.0128)

.0128=8(5^-4)=8(1/625)=128/10000

y intercept =8

horizontal asymptote is the x axis, y=0

range is (0,infinity), y>0