Answer:
It took 17 days for the pasture to be one-third covered in grass
Step-by-step explanation:
* Lets explain how to solve the problem
- The number of blades of grass is triple every day
- Consider that there are x blades in the first day
∵ The number of blades of grass is triple every day
∴ The next day the number of blades of grass will be 3x
∴ The formula to find the number of blades of grass after d days is
![x(3)^{d}](https://tex.z-dn.net/?f=x%283%29%5E%7Bd%7D)
- After 18 days, the entire pasture is completely covered in grass
∵ d = 18
∴ The number of blades of grass = ![x(3)^{18}](https://tex.z-dn.net/?f=x%283%29%5E%7B18%7D)
- We need to know the the number of days that took for the pasture
to be one-third covered in grass
∵ The number of blades of grass for 1/3 covered = ![(\frac{1}{3})x(3)^{18}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29x%283%29%5E%7B18%7D)
∴ ![(\frac{1}{3})x(3)^{18}=x(3)^{d}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29x%283%29%5E%7B18%7D%3Dx%283%29%5E%7Bd%7D)
- Remember ![\frac{1}{3}=3^{-1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%3D3%5E%7B-1%7D)
∴ ![3^{-1}x(3)^{18}=x(3)^{d}](https://tex.z-dn.net/?f=3%5E%7B-1%7Dx%283%29%5E%7B18%7D%3Dx%283%29%5E%7Bd%7D)
- Remember we add the power of the same bases when we
multiply them
∴
⇒ divide both sides by x
∴ ![(3)^{17}=(3)^{d}](https://tex.z-dn.net/?f=%283%29%5E%7B17%7D%3D%283%29%5E%7Bd%7D)
- Remember if the two bases equal in the equation, then their
powers are equal
∴ d = 17
* It took 17 days for the pasture to be one-third covered in grass