math problem for an interview

Question

Imagine a new pasture with grass growing on it. Every day after the seeds have germinated, the number of blades of grass in the pasture triples. After 18 days, the entire pasture is completely covered in grass. How many days did it take for the pasture to be one-third covered in grass? *

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Answer 1

Let's assume your field is 1000 ft² (I could choose any size!)

at the end of day 1 let the number of grass blades = x then

at the end of day 2 the number of grass blades = 3x

at the end of day 3 the number of grass blades = 9x (you can see the trend!) and after 18 days

at the end of day 18 the number of grass blades = 3^(18-1)x or 3^(Days-1)x now the field is covered at 1000 ft²

So, 3⁽¹⁷⁾x = 1000 or x = 7.744 x 10^(-6)

But when the field is 1/3 covered, it is 333.333 ft² covered So, 3^yx = 333.333

Then 3^y(7.744 x 10^(-6)) = 333.333 Solving for y we find that 3^y = 43046678 & y = 16

But the equation was 3^(Days-1) so y = Days - 1 = 16 and Days = 17

Therefore, the number of days for the field to be 1/3 covered is 17 out of 18 days. This does seem reasonable since at the end of the next day, 3(1/3) = 3(333.333) = 1000 ft² of the area will be covered!