State whether the following statement is true or false, and explain why, If the

Question

State whether the following statement is true or false, and explain why, If the statement is false, state the true change the naoral economy shrank at an annual rate of 5% per year for four consecutive years, then the economy shrank by 20% over the four-year period. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The statement is true because 4 x 5% is 20%. B. The statement is false because each year there is a different reference value. The economy actually shrank by Type an integer or decimal rounded to the nearest tenth as needed 41% er the ur-year period.

Explanation / Answer

The given statement is false as the reference value is different every year.

Let us consider initial the size of economy was 100 units and in year 1 economy shrank by 5%.

Hence at the end of year 1, the size of economy would be 100*0.95 = 95 units

Similarly, at the end of year 2, size of economy would be 95*0.95 = 90.25 units

At the end of 3rd year, 90.25*0.95 = 85.7375 and for 4th year it is 81.4506 units

Economy actually shrank by (100 - 81.4506) = 18.5%

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