a painter is painting a wall with an area of 150 ft². he decides to paint half of the wall and then take a…
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?\n112.50 ft²\n145.31 ft²\n147.66 ft²\n290.63 ft²
Answer
Explanation:
Step1: Find the remaining unpainted area formula
The initial area of the wall is $A = 150$ square - feet. After the first break, the remaining unpainted area is $A_1=\frac{1}{2}\times150$. After the second break, the remaining unpainted area is $A_2=\frac{1}{2}\times\frac{1}{2}\times150=\left(\frac{1}{2}\right)^2\times150$. In general, after $n$ breaks, the remaining unpainted area is $A_n=\left(\frac{1}{2}\right)^n\times150$.
Step2: Calculate the remaining unpainted area after 5 breaks
When $n = 5$, $A_5=\left(\frac{1}{2}\right)^5\times150=\frac{150}{32}=4.6875$ square - feet.
Step3: Calculate the painted area
The painted area $P$ is the initial area minus the remaining unpainted area. So $P = 150−A_5=150 - 4.6875=145.3125\approx145.31$ square - feet.
Answer:
145.31 ft²