In some country the average annual growth rate of GDP was 5% in each of the first 42 years, and in each of the next 35 years was 6%. By how much...

Hello!

If a constant annual growth rate of GDP is known, the rule of 70 gives an approximation of how many years it will take to double GDP. Specifically,

As you understand, actually take of both sides and obtain or    For small 's it is approximately

In our problem, so GDP will double after about years. It will double...

Hello!

If a constant annual growth rate of GDP is known, the rule of 70 gives an approximation of how many years it will take to double GDP. Specifically,

As you understand, actually take of both sides and obtain or    For small 's it is approximately

In our problem, so GDP will double after about years. It will double times, i.e. will be multiplied by

After that, and GDP will double after about years. Thus GDP will double times and will be also multiplied by

The combined growth will be = 64 times (using the 70 rule). Actually it will be 60 times.

And putting this in terms of percents we get growth by 64 times equals:

  6300%.

Or growth by 60 times is 5900%