8.2 Relative Rates of Growth
Finney Demana Waits Kennedy Text
Objectives:
•Comparing Rates of Growth
•Using L’Hopital’s Rule to Compare Growth
Rates
Why? Understanding growth rates as x->∞
is an important feature in understanding the
behavior of functions.
Essential Question:
Can I determine which function
growth faster or slower?
Conclusion: The functions grow at the
same rate. The degree of the functions
were the same. The constant had no
affect on the comparison.
Conclusion: The exponential
dominated the power function in the
denominator. The numerator was
growing faster than the denominator.
Conclusion: Exponentials grow faster
than power functions. The two
exponentials grow at the same rate
even with different bases.
Conclusion: Power Functions grow
faster than logarithmic functions.
Conclusion: The two functions grow at
the same rate. Both had a dominate
power function of the same degree.
Conclusion: The two functions grow at
the same rate even though the bases
were different. The predominate
function in both were logarithms.
Conclusion: The two functions grow at
the same rate. The degree of each
function was the same as h(x) = x.