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.