Question

at the beginning of the summer, there are 9 rabbits living in a field. each week for the rest of the summer, another rabbit moves in. define a unit for the amount of time since summer started. enter a variable for the amount of time since summer started and use this variable to write an expression for the number of rabbits living in the field. 1. how many rabbits will be living in the field 35 days after summer starts? 2. when there are 16 rabbits living in the field, how many weeks has it been? after completing the worksheet, graph your model.

Explanation:

Step1: Define Variables and Expression

Let \( t \) be the time in weeks since summer started. The initial number of rabbits is 9, and each week 1 more rabbit moves in. So the number of rabbits \( R \) is given by the expression \( R = 9 + t \).

Step2: Solve Question 1

We need to find the number of rabbits 35 days after summer starts. First, convert 35 days to weeks: \( 35 \div 7 = 5 \) weeks. Substitute \( t = 5 \) into the expression: \( R = 9 + 5 = 14 \). Wait, no, wait—wait, the problem says "another rabbit moves in each week". Wait, initial is 9, each week +1? Wait, maybe I misread. Wait, the problem says "At the beginning of the summer, there are 9 rabbits... Each week for the rest of the summer, another rabbit moves in." So the number of rabbits \( R = 9 + t \), where \( t \) is weeks. So 35 days is 5 weeks. So \( R = 9 + 5 = 14 \)? Wait, but maybe I made a mistake. Wait, no, let's check again. Wait, 35 days is 5 weeks (since 7 days a week). So \( t = 5 \), so \( R = 9 + 5 = 14 \).

Step3: Solve Question 2

We need to find \( t \) when \( R = 16 \). Set up the equation \( 16 = 9 + t \). Subtract 9 from both sides: \( t = 16 - 9 = 7 \) weeks.

Answer:

1. 14 rabbits
2. 7 weeks