A botanist measures a plant, in feet, at the beginning of each month and notices that the measurements form a geometric sequence, as shown below. 2, 2.2, 2.42, 2.662, ... If the first measurement was taken on September 1, about how tall was the plant three months before, on June 1, assuming the same growth pattern? A) 0.9 ft B) 1.5 ft C) 1.7 ft D) 2.0 ft

QUESTION POSTED AT 02/06/2020 - 01:35 AM

Answered by admin AT 02/06/2020 - 01:35 AM

Answer: Choice B) 1.5 ft

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Work Shown:

r = common ratio
r = (second term)/(first term)
r = 2.2/2
r = 1.1
Each term is multiplied by 1.1 to get the next term
Eg: 
term 2 = 1.1*(term 1)
term 2 = 1.1*2
term 2 = 2.2

Let x be the value three slots before the value 2
So we have x, x*r, x*r^2, x*r^3 where
x = value in June
x*r = value in July
x*r^2 = value in August
x*r^3 = value in September

We just found that r = 1.1. We also know that the value in September is 2. So this means

x*r^3 = 2
x*(1.1^3) = 2
x*1.331 = 2
x*1.331/1.331 = 2/1.331
x = 1.5026 approximately

This rounds to 1.5
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