Successive Percentage Changes

Successive Percentage Changes Consider the following tree which was originally 2 m high. After the first year, its height has increased by 2%, and after the second year, its height has further increased by 5%. How high is the tree after two years? Increased by 5% ? Increased by 2% 2 m After the 1st year After the 2nd year This question involves successive percentage changes.

From the previous page, the height of the tree after one year = 2  (1 + 2%) m = 2  1.02 m = 2.04 m the height of the tree after two years = 2.04  (1 + 5%) m = 2.04  1.05 m = 2.142 m Or we can simply write… the height of the tree after two years = 2  (1 + 2%)  (1 + 5%) m = 2  1.02  1.05 m = 2.142 m

Follow-up question 1. The price of a toy car was $200 in 2008. In 2009 and 2010, the price was increased by 10% and 20% respectively. Find the price of the toy car in 2010. Solution The price of the toy car in 2010 20%) (1 10%) $200 + × = 1.2 1.1 $200 × = $264 =

Follow-up question (cont’d) 2. Mary’s weight is 40 kg now. If her weight was decreased by 3% 2 years ago and then further decreased by 4% last year, find her weight 2 years ago. (Give your answer correct to 2 decimal places.) Solution Let x kg be Mary’s weight 2 years ago. 40 4%) (1 3%) = - × x 0.96 0.97 40 ¸ = x d.p.) 2 to (cor. 42.96 = ∴ Mary’s weight was 42.96 kg 2 years ago.