Two functions f and g are given. Show that the growth rate of the linear function is constant and that the relative growth rate of the exponential function is constant. f(t)equals160plus8.5t, g(t)equals160 e Superscript t divided by 8 What is the growth rate of the linear function
1 answer:
Answer:
linear function growth rate: 8.5
Step-by-step explanation:
The growth rate of the linear function is the coefficient of t: 8.5 . (It is a constant.)
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The growth rate of g(t) is its derivative: g'(t) = (1/8)(160e^(t/8)) = 20e^(t/8). Then the relative growth rate is ...
g'(t)/g(t) = (20e^(t/8))/(160e^(t/8)) = 20/160 = 1/8
It is a constant.
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