A park district paid their director $19,500 in 1960. In 2000 that same park district paid their director $40,000. Determine the average rate of increase per year to the nearest tenth of a percent
This is my answer
40,000-19,500=20,500/100=205%
is this correct?
It said PER YEAR
so divide by the number of years.
Also they asked for the rate of increase, not what percent the final figure is of the first one. Subtract 100% from the final to get the increase over the original.
Your 205 % is really 105 percent increase.
If you double something, that is 100% increase, not 200%.
Besides that, you performed a meaningles calculation.
The percentage increase is the
increase/original
= 2050019500
= 1.05
= 105% for the 40 years.
So the annual rate of salary increase
= 105% / 40 = 2.63%
you divided 20500 by 100
To determine the average rate of increase per year, we need to find the percentage increase from 1960 to 2000 and then divide it by the number of years.
First, let's find the percentage increase from $19,500 to $40,000:
Increase = $40,000 - $19,500 = $20,500
Percentage Increase = (Increase / Initial Amount) * 100
= ($20,500 / $19,500) * 100 ≈ 105.13%
Now, to find the average rate of increase per year, we need to divide the percentage increase by the number of years:
Number of Years = 2000 - 1960 = 40 years
Average Rate of Increase per Year = Percentage Increase / Number of Years
= 105.13% / 40
≈ 2.63%
So, the average rate of increase per year is approximately 2.63%.