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A tree is 4 1/2 feet tall. It is expected to grow 1 3/4 feet per year. At this growth rate, how many years will it take for the tree to have a height greater then 40 feet?

User Jhilom
by
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1 Answer

2 votes

Answer:

21 years

Explanation:

Given


Initial\ Height = 4(1)/(2)


Final\ Height = 40


Difference = 1(3)/(4)

Required

Determine the years it'll take to grow to the final height

This question depicts arithmetic progression and will be solved using


T_n = a + (n - 1)d

Where


T_n = 40


a = 4(1)/(2)


d = 1(3)/(4)

Substitute these values in the given formula;


40 = 4(1)/(2) + (n - 1)1(3)/(4)

Convert all fractions to decimal


40 = 4.5 + (n - 1) * 1.75

Open Brackets


40 = 4.5 + 1.75n - 1.75

Collect Like Terms


1.75n = 40 - 4.5 + 1.75


1.75n = 37.25

Divide both sides by 1.75


n = (37.25)/(1.75)


n = 21.2857142857


n = 21 (Approximated)

User Janux
by
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