Carmelita is planning to swim in a charity swim- a- thon. several relatives said they would sponsor her.

Grandmother: I will give you $1 if you swim 1 lap,$3 if you swim 2 laps, $5 if you swim 3 laps,$7 if you swim 4 laps, and so on.

Father: I will give you $1 if you swim 1 lap,$3 if you swim 2 laps, $9 if you swim 3 laps,$27 if you swim 4 laps, and so on.

Aunt Josie: I will give you $2 if you swim 1 lap,$3.50 if you swim 2 laps, $5 if you swim 3 laps,$6.50 if you swim 4 laps, and so on.

Uncle Sebastian: I will give you $1 if you swim 1 lap,$2 if you swim 2 laps, $4 if you swim 3 laps,$8 if you swim 4 laps, and so on.

For each relative, write an equation for the total donation d if Carmelita swims n laps. Which variable is the independent variable? Dependent variable?

Zak's uncle wants to donate money to Zak's school. He suggests three possible plans. Look for a pattern in each plan.

Are any of the relationships in Plans 1,2, or 3 exponential functions? Explain.

Plan 1: He will continue the pattern in this table until day 12.

School Donations

Plan 2: He will continue the pattern in this table until day 10.

School Donations

Plan 3: He will continue the pattern in this table until day 7.

School Donations

Zak's uncle wants to donate money to Zak's school. He suggests three possible plans. Look for a pattern in each plan.

For each plan, write an equation for the relationship between the day number n and the number of dollars donated d.

Plan 1: He will continue the pattern in this table until day 12.

School Donations

Plan 2: He will continue the pattern in this table until day 10.

School Donations

Plan 3: He will continue the pattern in this table until day 7.

School Donations

Zak's uncle wants to donate money to Zak's school. He suggests three possible plans. Look for a pattern in each plan.

Copy and extend each table to show how much money the school would receive each day.

Plan 1: He will continue the pattern in this table until day 12.

School Donations

Plan 2: He will continue the pattern in this table until day 10.

School Donations

Plan 3: He will continue the pattern in this table until day 7.

School Donations

Many single-celled organisms reproduce by dividing into two identical cells. Suppose an amoeba (uh MEE buh) splits into two amoebas every half hour.

A biologist starts an experiment with one amoeba. Make a graph of the data (time, amoebas), showing the number of amoebas she would have at the end of each hour over an 8-hour period.

Many single-celled organisms reproduce by dividing into two identical cells. Suppose an amoeba (uh MEE buh) splits into two amoebas every half hour.

How many hours will it take for the number of amoebas to reach one million?

Many single-celled organisms reproduce by dividing into two identical cells. Suppose an amoeba (uh MEE buh) splits into two amoebas every half hour.

Write an equation for the number of amoebas a after t hours. Which variable is the independent variable? Dependent variable?

Many single-celled organisms reproduce by dividing into two identical cells. Suppose an amoeba (uh MEE buh) splits into two amoebas every half hour.

A biologist starts an experiment with one amoeba. Make a table showing the number of amoebas she would have at the end of each hour over an 8-hour period.

What is the smallest value of n that your calculator will display in scientific notation?

a. $10^n$

b. $100^n$

c. $1000 n^n$

What is the largest whole-number value of n that your calculator will display in standard notation?

a. $3^n$

b. $\pi^n$

c. $12^n$

d. $237^n$

Write the following number in standard form.

$$3.4348567000 \times 10^{10}$$

Describe an exponential growth pattern. Include key properties such as growth factors.

What other Mathematical Practices can you identify in Tori's reasoning given below?

We wrote the equation, $r=\frac{1}{2} 2^n$ to represent the relationship between the number of rubas, r on square n in the problem. As the number of squares increase by 1 , the number of rubas doubles.

We went backwards in the table to find the number of rubas on square 0. To find the number of rubas on square 0, we divided the number of rubas on square 1 by 2. One divided by two is $\frac{1}{2} \cdot \frac{1}{2}$ is the y-intercept.

If you start with square 0, you get the number of rubas on the next square by multiplying the number of rubas on square 0 by 2 . This process is repeated for the next square, etc. So, on square n, you multiply $\frac{1}{2}$ by $2, n$ times. $\frac{1}{2} \times 2 \times 2 \times \ldots \times 2$ or $\frac{1}{2}\left(2^n\right)$

Describe the pattern of change? How many ballots are there after the n cuts?