Final answer:
To find out how tall a bamboo plant will be in 13 days considering it grows in an arithmetic sequence, we identify the common difference and apply the formula An = A1 + (n - 1) * d. With a starting height of 130 inches and a common difference of 13 inches per day, the plant will be 299 inches tall in 13 days.
Step-by-step explanation:
The question involves finding a rule to represent the height of a bamboo plant as it grows over time, which is an example of an arithmetic sequence in mathematics. An arithmetic sequence is a sequence of numbers such that the difference of any two successive members is a constant, known as the common difference. In this case, the bamboo plant grows by the same amount each day.
The heights of the bamboo plant provided are 130 inches, 143 inches, 156 inches, and 169 inches. We can see that the plant is growing by 13 inches each day since 143 - 130 = 13, 156 - 143 = 13, and 169 - 156 = 13. Thus, the common difference is 13 inches.
The general rule for an arithmetic sequence can be written as An = A1 + (n - 1) * d, where An is the height on the n-th day, A1 is the initial height (on the first day), n is the number of days, and d is a common difference.
Using this formula, the height of the bamboo plant after 13 additional days would be:
A1 = 130 inches (initial height)
d = 13 inches (common difference)
n = 1 + 13 = 14 (since we're including the current day plus 13 additional days)
An = 130 + (14 - 1) * 13
An = 130 + 13 * 13
An = 130 + 169
An = 299 inches
Therefore, the bamboo plant will be 299 inches tall after 13 more days.