Question

Tree Height Problem Assume that the number of inches a tree grows (up) each year is a term in a geometric series. Suppose that you plant a tree that grows 40 inches the first year and 38 inches the next year. a. Predict how much it will grow the 5th year. b. Predict how tall it will be after 10 years. c. Predict the ultimate height it will reach.

Answer 1

Based on the growth difference between year 1 and year 2, and the fact that it follows a geometric series, the growth of a given year is 95% of the previous year.

To express growth as a function of time:

G(t) = 40*(.95)^(t-1) , where t is the year

Year 1:

G(1) = 40*.95^0 = 40 This is the growth in the first year

G(2) = 40 * .95^1 = 38

G(5) = 40 * .95^4 = 32.58

Adding 10 years:

40 + 38 + 36.1 + 34.3 + 32.58 + 30.95 + 29.4 + 27.93 + 26.54 + 25.21 =

321.01 inches

The tree will reach a maximum of 800 inches

Hope this helps :)

Answer 2

Based on the growth difference between year 1 and year 2, and the fact that it follows a geometric series, the growth of a given year is 95% of the previous year.
To express growth as a function of time:
G(t) = 40*(.95)^(t-1) , where t is the year
Year 1:
G(1) = 40*.95^0 = 40 This is the growth in the first year
G(2) = 40 * .95^1 = 38
...
G(5) = 40 * .95^4 = 32.58

Adding 10 years:
40 + 38 + 36.1 + 34.3 + 32.58 + 30.95 + 29.4 + 27.93 + 26.54 + 25.21 =
321.01 inches

The tree will reach a maximum of 800 inches