To determine which answer choice represents the exponential function that matches the table, we can plug in the given x values into the answer choices and see which ones match the corresponding f(x) values provided in the table.
For x = 1:
f(x) = 15(4/3)^1 = 15(4/3) = 20
f(x) = 16(3/4)^1 = 16(3/4) = 12
f(x) = 64(4/3)^1 = 64(4/3) = 85.33
f(x) = 64(3/4)^1 = 64(3/4) = 48
For x = 2:
f(x) = 15(4/3)^2 = 15(16/9) = 26.67
f(x) = 16(3/4)^2 = 16(9/16) = 9
f(x) = 64(4/3)^2 = 64(16/9) = 113.78
f(x) = 64(3/4)^2 = 64(9/16) = 36
For x = 3:
f(x) = 15(4/3)^3 = 15(64/27) = 35.56
f(x) = 16(3/4)^3 = 16(27/64) = 6.75
f(x) = 64(4/3)^3 = 64(64/27) = 150.52
f(x) = 64(3/4)^3 = 64(27/64) = 27
For x = 4:
f(x) = 15(4/3)^4 = 15(256/81) = 47.41
f(x) = 16(3/4)^4 = 16(81/256) = 5
f(x) = 64(4/3)^4 = 64(256/81) = 201.78
f(x) = 64(3/4)^4 = 64(81/256) = 20.25
Based on the calculations, the only answer choice that matches the f(x) values in the table is:
f(x) = 64(3/4)^x
Therefore, the exponential function that matches the table is f(x) = 64(3/4)^x.
The table represents some points on the graph of an exponential function.
table
x f(x)
1 48
2 36
3 27
4 20.25
answer choices
f(x)=15(4/3)^x
f(x)=16(3/4)^x
f(x)=64(4/3)^x
f(x)=64(3/4)^x
1 answer