f(x)=k(1.44) x The function f is defined by the given equation, where k is a constant. The value of f(x) increases by p% for every increase of x by 1 . For which of the following functions, where k is a constant, does the value of g(x) increase by p% for every increase of in x by 31 ?
Question
f(x)=k(1.44) x The function f is defined by the given equation, where k is a constant. The value of f(x) increases by p% for every increase of x by 1 . For which of the following functions, where k is a constant, does the value of g(x) increase by p% for every increase of in x by 31 ?
Solution
The function g(x) that increases by p% for every increase in x by 1/3 is g(x) = k(1.44)^(3x).
Here's why:
In the original function f(x) = k(1.44)^x, the value of f(x) increases by p% for every increase of x by 1. This is because the base of the exponent, 1.44, represents a 44% increase (or p% increase) for each unit increase in x.
If we want a function g(x) that increases by the same p% for every increase in x by 1/3, we need to adjust the exponent in the function to account for this.
We do this by multiplying x by 3 in the exponent, giving us g(x) = k(1.44)^(3x). Now, for every increase in x by 1/3, the value of g(x) will increase by p%, the same rate of increase as in the original function f(x).
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