Question

As x approaches ∞, which statement BEST compares these functions?
Responses
A The linear function will eventually exceed the exponential function.The linear function will eventually exceed the exponential function.
B The exponential function will eventually exceed the linear function.The exponential function will eventually exceed the linear function.
C The exponential function will exceed the linear function because is has a lower initial value.The exponential function will exceed the linear function because is has a lower initial value.
D The linear function will exceed the exponential function because is has a greater initial value.The linear function will exceed the exponential function because is has a greater initial value.
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Answer 1

B

Exponential functions grow much faster than linear ones as x → ∞, so eventually the exponential will exceed the linear. (Equivalently, for a linear L(x)=ax+b and an exponential E(x)=c·d^x with d>1, lim_{x→∞} L(x)/E(x)=0.)