19 Mark for Review The value of an autographed baseball increased by \( 178 \% \) from the end of 2012 to the end of 2013 and then decreased by \( 21 \% \) from the end of 2013 to the end of 2014 . What was the net percentage increase in the value of the autographed baseball from the end of 2012 to the end of 2014 ? (A) \( 119.62 \% \)

Let the value of the baseball at the end of 2012 be \( V \). 1. From the end of 2012 to the end of 2013, the value increased by \( 178\% \). This means the new value is \[ V \times (1 + 1.78) = V \times 2.78. \] 2. From the end of 2013 to the end of 2014, the value decreased by \( 21\% \). The new value is then \[ V \times 2.78 \times (1 - 0.21) = V \times 2.78 \times 0.79. \] 3. Calculate the net multiplier: \[ 2.78 \times 0.79 = 2.1962. \] So, the value at the end of 2014 is \[ V \times 2.1962. \] 4. The net increase in value from the end of 2012 is obtained by subtracting the original value \( V \): \[ V \times 2.1962 - V = V(2.1962 - 1) = V \times 1.1962. \] 5. Converting the net increase into a percentage: \[ 1.1962 \times 100\% = 119.62\%. \] Thus, the net percentage increase in the value of the autographed baseball is \( 119.62\% \).