which grows faster linear or exponential
Mathematics · High School · Sun Jan 24 2021
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In mathematics, when comparing the growth of linear functions to exponential functions, exponential functions grow much faster than linear functions after a certain point.
A linear function has the form y = mx + b, where `m` is the slope and `b` is the y-intercept. This means that as you increase x by one unit, y increases by a constant amount, `m`. The growth is steady and predictable.
On the other hand, an exponential function has the form y = a * b^x, where `a` is a constant, and `b` is the base of the exponential. The value of `y` increases by a factor of `b` as `x` increases by one. This means the growth rate is not constant but instead increases as the value of `x` gets larger—the growth is multiplicative.