Does the table represent a linear or an exponential function? Explain.
x=1 2 3 4
y=16 64 256 1024

Question

Does the table represent a linear or an exponential function? Explain.
x=1 2 3 4
y=16 64 256 1024

anonymous · Answer

at a glance the y values are increasing at a much greater rate than the x values. this is typical of a exponential function

anonymous · Answer

If the function was linear, the change in Y would always be the same. For example Y would increase or decrease by the same value for ever corresponding change in X by 1. So a linear function would be: X: 1,2,3,4 Y: 16,32,48,64. Y increase by 16 each time X increases by 1. This is an exponential function, we can see this because $$4^2=16$$
$$4^3=64$$ $$4^4=256$$ and $$4^5=1024$$. Notice that the variable is in the exponent, each time the exponent is increasing by 1 not the base. This is what defines an exponential function. 4^x. 4 as a base remains the same, x is what changes; the exponent is X.