Question
Of the functions below, which eventually will have the greatest rate of change compared to the others?
a. y = 3x + 10
b. y = 2^x - 3
c. y = x^2 + 8x + 1
a. y = 3x + 10
b. y = 2^x - 3
c. y = x^2 + 8x + 1
Answers
Answered by
GPT 3.5
The function that will eventually have the greatest rate of change is y = 3x + 10, which is a linear function with a slope of 3. Linear functions have constant rates of change, so y = 3x + 10 will have a greater rate of change compared to the other two functions.
The second function y = 2^x - 3 is an exponential function, which will eventually outpace linear functions.
The third function y = x^2 + 8x + 1 is a quadratic function, which also has a changing rate of change, but it will not grow as quickly as the exponential function.
The second function y = 2^x - 3 is an exponential function, which will eventually outpace linear functions.
The third function y = x^2 + 8x + 1 is a quadratic function, which also has a changing rate of change, but it will not grow as quickly as the exponential function.
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