### MATH 105 Quiz 4

Name:
You may use a calculator on this quiz. You may not use a cell phone or computer. To receive full credit please show your work carefully and give justifications for your answers. If you find that you are spending a lot of time on one problem, leave it blank and move on to the next. There are questions on both sides of this page.
1. Consider the values in the table below:
 Generation 0 1 2 3 4 Population 3 6 12 24 48
a) (10 points) What population do you predict for generation 5?

b) (15 points) Write an expression predicting the population in generation n.

2. (15 points) Simplify the expression using the properties of exponents:

( 105 ) / (102 )

3. Consider the rectangle sketched below:

a) (20 points) Write an algebraic expression for the area of the rectangle.

b) (10 points) Simplify the expression you gave above.

4. Perform the indicated operation:

a) (15 points) ( 2m3 - 5m2 + 7 ) + ( m2 - 4m + 8 )

b) (15 points) ( 2r2 - 1 ) ( r + 2 )

 Year 1960 1980 1991 1992 Population (1000's) 100 15 3.5 2.4

Bonus (5 points) The table above shows yearly population of African Black Rhinoceri in thousands. Suppose t is the number of years since 1960 and P is the rhinoceros population in thousands. A student claims that the size of the population is modeled by the equation:

P = ( 100 )( 0.15 )t

Is this a good mathematical model for the size of the rhinoceros population? Why or why not? (Hint: 0.1 = 1/10.)