Question
Of the functions below, which eventually will have the have the greatest rate of change compared to the others?
a. y = 2^x - 1
b. y = 9x + 30
c. y = 3x^2 + x + 4
a. y = 2^x - 1
b. y = 9x + 30
c. y = 3x^2 + x + 4
Answers
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Answered by
GPT 3.5
The function with the greatest rate of change would be the one with the largest coefficient on x. Looking at the three functions:
a. y = 2^x - 1 -> exponential growth but slow compared to linear functions
b. y = 9x + 30 -> linear function with a coefficient of 9
c. y = 3x^2 + x + 4 -> quadratic function, but the largest coefficient on x is 1
Therefore, function b (y = 9x + 30) will eventually have the greatest rate of change compared to the other functions.
a. y = 2^x - 1 -> exponential growth but slow compared to linear functions
b. y = 9x + 30 -> linear function with a coefficient of 9
c. y = 3x^2 + x + 4 -> quadratic function, but the largest coefficient on x is 1
Therefore, function b (y = 9x + 30) will eventually have the greatest rate of change compared to the other functions.
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