Determine whether the following statement is true or false and then explain wit an example: to downturn the a small town in Nevada lost 20% of its population. However, after a significant improvement in the economy, this same town then gained 20% more people. In the end the town's population was the same as it was before the downturn."

Of course, this statement is FALSE.
Lets assume that a small town in Nevada had a population of 1,000. When it lost 20% of its population: 1,000 ( 1 - 0.2 ) = 1,000 - 0.8 = 800 After that the same town gained 20 % more people: 800 ( 1 + 0.2 ) = 800 * 1.2 = 960 960 ≠ 1,000 In the end the towns population was not the same as it was before the downturm.

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Edufirst Edufirst · Answer 2 · 2016-10-05T05:37:25-04:00

False.

The first time, when the small towm 20%, the decrease is calculated over the intial population. So the lost is 20% of initial poulation = 0.2 initial population. And the new population will be 0.8initial population.

Second time, the increase is calculates over the new population. The gain is 20% of then new popultion = 0.2new population = 0.20.8initial population = 0.16 initial population.

Then while the loss was 0.2 initial population the gain was 0.16initial population, being the gain less than the loss. So, at the end the town's population was less than before the downturn.

When you use percentages you have to be aware that the base over which they are calculated determines ther result. A lower base turns into a greater %.