Question

a nature preserve opened with a population of 6 rabbits. after one year, the number of rabbits had doubled. the year after that, the number of rabbits doubled once again. assuming that this pattern continues, plot the solution points for the first three years along with the y-intercept. let y represent the number of rabbits on the nature preserve after x years.

Explanation:

Step1: Identify initial point (y-intercept)

The nature preserve opened with 6 rabbits at \( x = 0 \) (year 0). So the point is \( (0, 6) \).

Step2: Calculate population after 1 year

After 1 year (\( x = 1 \)), the population doubled. So \( y = 6\times2 = 12 \). The point is \( (1, 12) \).

Step3: Calculate population after 2 years

After 2 years (\( x = 2 \)), the population doubled again. So \( y = 12\times2 = 24 \). The point is \( (2, 24) \).

Step4: Calculate population after 3 years

After 3 years (\( x = 3 \)), the population doubled again. So \( y = 24\times2 = 48 \). The point is \( (3, 48) \).

To plot the points:

• For \( (0, 6) \): Find \( x = 0 \) (the y - axis) and \( y = 6 \) on the graph and mark the point.
• For \( (1, 12) \): Find \( x = 1 \) on the x - axis and \( y = 12 \) on the y - axis and mark the point.
• For \( (2, 24) \): Find \( x = 2 \) on the x - axis and \( y = 24 \) on the y - axis and mark the point.
• For \( (3, 48) \): Find \( x = 3 \) on the x - axis and \( y = 48 \) on the y - axis and mark the point.

Answer:

The points to plot are \((0, 6)\), \((1, 12)\), \((2, 24)\), and \((3, 48)\).