### 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.

- 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.

- (15 points) Simplify the expression using the properties of exponents:
( 10^{5} ) / (10^{2} )

- 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.

- Perform the indicated operation:
a) (15 points) ( 2m^{3} - 5m^{2} + 7 ) + (
m^{2} - 4m + 8 )

b) (15 points) ( 2r^{2} - 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.)