Question

At the end of week one, a stock had increased in value from $5.75 a share to $7.50 a share. Find the percent of increase at the end of week one to the nearest tenth of a percent. At the end of week two, the same stock had decreased in value from $750 to $5.75. Is the percent of decrease at the end of week two the same as the percent of increase at the end of week one? Justify your answer.

Answer 1

To calculate the percentage we will use the following formula: (final value-initial value)/initial value.

In our case the inital value is 5.75 and the ending value is 7.5

then the percentage change is

`(7.5-5.75)/(5.75)=0.3043`

this corresponds to an increase of 30.43%

In the second case, the initial value is 7.5, so ieven though the change is mostly the same, the reference value to which we are calculating the percentage is not the same, hence the percentage value is not the same. We confirm this by calculating

`(5.75-7.5)/(7.5)=\text{ }-0.2333`

which corresponds to a decrease of 23.33%