Question

A redwood tree in King’s Canyon National Park, California has a circumference of 220 inches. Tanner measured the circumference of some other redwoods that had been planted over the last 5 years. His data is recorded below. Write a rule for the data in the table.

Use your rule to predict the circumference of a tree after 50 years of growth.
Use your rule to estimate the age of the tree with a circumference of 221 inches.

Answer 1

The rule for the data is: Circumference = 220 + 16 * years. The predicted circumference of the tree after 50 years of growth is 1020 inches. The estimated age of the tree with a circumference of 221 inches is approximately 23 days.

Step-by-step explanation:

To write a rule for the data, we need to look for a pattern. The data suggests that the circumference of the redwood tree is increasing at a constant rate over time. Let's calculate the rate of increase by finding the difference between the circumference after 5 years (300 inches) and the circumference after 0 years (220 inches). The difference is 80 inches over a span of 5 years, so the rate of increase is 80 inches / 5 years = 16 inches per year. Therefore, the rule for the data is: Circumference = 220 + 16 * years.

To predict the circumference after 50 years of growth, we substitute years = 50 into the rule: Circumference = 220 + 16 * 50 = 220 + 800 = 1020 inches.

To estimate the age of the tree with a circumference of 221 inches, we use the rule to solve for years: 221 = 220 + 16 * years. Rearranging the equation, we get: 16 * years = 1. Solving for years, we find that the tree has been growing for approximately 0.0625 years, or about 23 days.