Answer:
f(x) = 3.56(2.04)^x
Step-by-step explanation:
Put x as 2, to see whether the output will be close to 16.
116.4 - 42.8 ln(2) = 86.733301
2.04(3.56)^2 = 25.854144
3.56(2.04)^2 = 14.815296
-42.8 + 116.4 ln(2) = 37.882332
Put x as 3, to see whether the output will be close to 30.
116.4 - 42.8 ln(3) =69.379394
2.04(3.56)^3 = 92.040753
3.56(2.04)^3 = 30.223204
-42.8 + 116.4 ln(3) = 85.07847
Put x as 6, to see whether the output will be close to 271.
116.4 - 42.8 ln(6) = 39.712695
2.04(3.56)^6 = 4152.69615
3.56(2.04)^6 = 256.584846
-42.8 + 116.4 ln(6) = 165.760802
Put x as 7, to see whether the output will be close to 522.
116.4 - 42.8 ln(7) = 33.115046
2.04(3.56)^7 = 14783.598295
3.56(2.04)^7 = 523.433085
-42.8 + 116.4 ln(7) = 183.703941
The exponential function that models the data is f(x) = 3.56(2.04)^x.
