Question

A water lily covers 0.8m^2 of a pond. How much time did it take to cover the entire pond if we know that the water lily can double it’s surface area every month. The surface area of the bond is 409.6m^2

A) 8 months
B) 9 months
C) 10 months
D) 11 months
E) 12 months

Answer 1

Given info : A water lily covers 0.8m² of a pond. The surface area of the pond is 409.6m².

To find : How much time did it take to cover the entire pond if we know that the water lily can double it’s surface area every month.

solution : this question is based on Geometric progression.

here first term, a = 0.8 m²

last term, Tn = 409.6 m² [ because water lily has to cover entire surface area of pond. ]

common ratio , r = 2 [ ∵ every month, water lily become double of itself. ]

now using formula, Tn = arⁿ¯¹

⇒409.6 = 0.8 (2)ⁿ¯¹

⇒409.6/0.8 = (2)ⁿ¯¹

⇒512 = (8)³ = (2)ⁿ¯¹

⇒(2³)³ = (2)ⁿ¯¹

⇒2^9 = 2ⁿ¯¹

⇒9 = n - 1

⇒n = 10

Therefore after 10 months, water lily will cover entire surface area of pond.

Answer 2

Answer:

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