For a certain species of tree, the average height of the tree after 2 years is 3

Question

For a certain species of tree, the average height of the tree after 2 years is 3 feet, and after 6 years the height of the tree is 17 feet. Assume that the annual (a) Find the annual rate of change of the height of the tree in feet per year Annual rate of change feet year Suemit Arswer Tries 099 (b) Find a function for the height h of the tree in feet as a function of time t in years. (e) Find the domain of the function from part (b).Enter in interval notation. Domain:e Submit Answer Tries O/99 (d) How tall will the tree be after 17 years? fect e) After how many years will the tree be 23 feet tall? Round your answer to two decimal places years Submit Anse Tries or99

Explanation / Answer

(2,3),(6,17)

slope=(17-3)/(6-2)=14/4=3.5

a.Annual rate of change of height=3.5 feet/year

Using point slope form

h-3=3.5(t-2)

h=3.5t-4

c.Domain

time cant be less than 1 or greater than 30 according to question

Therefore domain [1,30]

d.h=3.5(17)-4=55.5 feet

e.23=3.5t-4

3.5t=19

t=5.43 years

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