A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?
112.50 ft2
145.31 ft2
147.66 ft2
290.63 ft2
Let's calculate the portion of the wall that the painter will have painted after each break:
- After the first break, the painter has painted 1/2 * 150 ft^2 = 75 ft^2.
- After the second break, the painter has painted 1/2 * (150 ft^2 - 75 ft^2) = 37.5 ft^2.
- After the third break, the painter has painted 1/2 * (150 ft^2 - 75 ft^2 - 37.5 ft^2) = 18.75 ft^2.
- After the fourth break, the painter has painted 1/2 * (150 ft^2 - 75 ft^2 - 37.5 ft^2 - 18.75 ft^2) = 9.375 ft^2.
Now, let's add up the areas of the painted portions:
75 ft^2 + 37.5 ft^2 + 18.75 ft^2 + 9.375 ft^2 = 140.625 ft^2.
Therefore, when the painter takes his fifth break, he will have painted approximately 140.625 ft^2 of the original wall.
None of the provided answer choices exactly matches this value, so we must round to the nearest option. The closest answer choice is 145.31 ft^2.