Graphing Exponential Functions, Logarithms, and Logarithmic Functions

Question

1. How does the graph of the following function behave as x increases? Use the ex button on the graphing calculator.

y = 2ex + 4

 

2. Find the domain & range of the following function:

y = 2(3 x - 1)

 

3. The population of Smartyville is 2002 was estimated to be 22,000 people with an anual rate of increase of about 2.5%.

a) What is the growth rate for Smartyville:

b) Write an equation to model future growth.

 

c) Use your equation to estimate the population in 2008 to the nearest hundred.

 

4. Rewrite log8 2 = 1/3 in exponential form

Answer 1

2^x + 4 gets unboudedly large as x gets large. So 2^x + 4  approaces infinity (positive)

 

y = 2(3x +1)

 

The domain is all real numbers

 

Since y = 6x - 2  (distributive law) it is a straight line spanning all real values for both x &y  the range is also al real numbers