A. Give Examples of Equations for Each of the Following Functions

Math 65. Section 3.6

I. Review

A. Give examples of equations for each of the following functions:

1. Linear: ______

2. Quadratic:______

3. Square Root: ______

4. Exponential: ______

B. Label each of the following graphs as linear, quadratic, square root or exponential.



  

   

   

   

                    

           

             

   

    

 II. General information about exponentials (8 characteristics to know):

3. M65, Sec. 3.6 pg 2 4.

III. Applications:

A. Given the model (equation) use it correctly to answer questions:

Ex. 1: A bacteria colony starts with 1000 bacteria and grows according to the following model, where t is the number of elapsed hours and P(t) is the population at time t. t P( t ) = 1000( 1.12) a) What was the starting number of bacteria? ______b) What is the base? ______. This indicates it is a growth/decay. c) Predict the number of bacteria after 10 hours: d) Predict the number of bacteria after 60 hours (2.5 days): M65, Sec. 3.6, pg 3 B. Given the information, organize it and come up with the model (equation) that describes the situation:

Ex. 2: The population in the US in 1995 was about 263 million. The growth rate was about 0.7% per year (less than 1 percent). Let t=0 represent 1995.

population (mils)

Find a model (equation) that fits this situation and use it to predict the population in 2005.

Ex. 3: In 1990, India had a population of 853.4 million. In 1991 the estimated population was 871.3 million. Assuming that populations grow exponentially, fill in the following table. Find a model to represent this situation. (Round your base to three decimal places). Use your model to predict the population for the year 2010 (round to the nearest tenth of a million).

population (mils) M65, Sec. 3.6, pg 4 Ex. 4. Atmospheric pressure at sea level is 14.7 psi (pounds per square inch). The atmospheric pressure drops exponentially as we move above sea level. At 1 mile above sea level the pressure is 14.4 psi. Fill in the following table and use it to find a model that represents this situation. (Round your base to 4 decimal places.) Use your model to predict the atmospheric pressure at the peak of Mt. Everest (about 5.5 miles above sea level).

altitude (miles) pressure (psi)