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
[tex]x(3)^{d}[/tex]
- After 18 days, the entire pasture is completely covered in grass
∵ d = 18
∴ The number of blades of grass = [tex]x(3)^{18}[/tex]
- 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 = [tex](\frac{1}{3})x(3)^{18}[/tex]
∴ [tex](\frac{1}{3})x(3)^{18}=x(3)^{d}[/tex]
- Remember [tex]\frac{1}{3}=3^{-1}[/tex]
∴ [tex]3^{-1}x(3)^{18}=x(3)^{d}[/tex]
- Remember we add the power of the same bases when we
multiply them
∴ [tex]x(3)^{-1+18}=x(3)^{d}[/tex] ⇒ divide both sides by x
∴ [tex](3)^{17}=(3)^{d}[/tex]
- 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
