The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x)=50+10logx. Suppose each of the x objects increases its sound power by 10 decibels, so that the new total sound power, in decibels, is given by the function g(x)=f(x)+10. Which shows the graphs of f of x and g of x ?
Answer
A
Image with description On a coordinate plane y = f (x) starts at (0, 50) and curves up through (10, 60). y = g (x) starts at (0, 40) and curves up through (10, 50).
B
Image with description On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).
Explanation
Since g(x) = f(x) + 10, the graph of g is the graph of f shifted up 10 units. At x = 1, log(1) = 0, so f(1) = 50 and g(1) = 60; at x = 10, both graphs rise by 10, giving f(10) = 60 and g(10) = 70. Choice B shows g consistently 10 units above f.
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