# Real Number and Function

Washington performance expectations assessed for purposes of graduation.

A1.1.A Select and justify functions and equations to model and solve problems.

1. Mrs. Morris gave her students this pattern of white tiles

She asked her students to write an equation to represent the number of white tiles, t, for any figure number, n. Which equation represents the number of white tiles in the pattern?

A. t = n + 2

B. t = n + 4

C. t = 4n + 4

D. t = 4n + 8

2. Kesha is planning to rent a van for her trip to Mt. Rainier. Two of her friends each rented the same type of van from the same car rental company last week. This is what they told her:

John: “The cost of my rental was $240. The company charged me a certain amount per day and a certain amount per mile. I had the rental for five days and I drove it 200 miles.”

Katie: “The cost of my rental was only $100. I drove it for 100 miles and had it for two days.”

Kesha plans to get the same type of van that John and Katie had from the same car rental company. Kesha estimated her trip would be 250 miles, and she would have the vehicle for four days.

Let C = cost, M = miles, and D = days

Which equation could Kesha use to figure out how much her rental would cost?

A. C = 40.00M + 0.20D

B. C = 40.00D + 0.20M

C. C = 20.00M + 0.40D

D. C = 20.00D + 0.40M

3. Joey earned money over the summer at different jobs and put all his money into savings. The table below shows how his total savings changed.

Weeks into the summer| 0| 1| 2| 3| 4| 5|

Total Savings ($)| 50| 135| 220| 305| 390| 475|

Write a function to model this situation. Be sure to define your variables.

4. Raven was selling cookies to raise money. She started off with 900 cookies. She sold an average of average of 75 cookies each day.

* Write a function to model the number of cookies left. Be sure to define your variables. * State an appropriate domain for your model.

5. Professor Plum conducted an experiment on the number of bacteria growing in his lab. The data below shows his results.

Day| 0| 1| 2| 3| 4| 5|

Approximate # of bacteria| 50| 100| 200| 400| 800| 1600|

Write a function to model this situation. Be sure to define your variables.

6. For the month of July, Michelle will be dog-sitting for her very wealthy, but eccentric, neighbor, Mrs. Buffett. Mrs. Buffett offers Michelle two different salary plans: — Plan 1: $100 per day for the 31 days of the month.

— Plan 2: $1 for July 1, $2 for July 2, $4 for July 3, and so on, with the daily rate doubling each day. * Write functions that model the amount of money Michelle will earn each day on Plan 1 and Plan 2. Justify the functions you wrote. * State an appropriate domain for each of the models based on the context. * Which plan should Michelle choose to maximize her earnings? Justify your recommendation mathematically. * Extension: Write an algebraic function for the cumulative pay for each plan based on the number of days worked.

7. Scientists in Australia have been watching the humpback whale population for many years. In 1981, they counted 350 whales off of the shoreline. Through the years, they continued to count and noticed that the number of whales increased by 12% each year. Write a function rule that describes the humpback whale population. (Be sure to define your variables.)

8. The number of bacteria growing in Professor Plum’s lab is recorded below. Day| 0| 1| 2| 3| 4| 5|

Bacteria| 1024| 1536| 2304| 3456| 5184| 7776|

Explain how you know the data is or is not exponential.

9. Josephine had $50 in savings at the start of the summer. She was able to save an additional $23 per week. Write a function to show the amount in savings, S, that Josephine will have after w weeks...

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