SOLUTION: There are currently 80 million cars in a country, decreasing 3.4% annually. How many years will it take for this country to have 58 million cars? Round to 3 decimal places.

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Question 1187748: There are currently 80 million cars in a country, decreasing 3.4% annually. How many years will it take for this country to have 58 million cars? Round to 3 decimal places.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If the number of cars is decreasing by 3.4% per year, then the number of cars remaining is getting multiplied by 100%-3.4% = 96.6% each year. With a current count of 80 million, the number of millions of cars after n years will be

80%280.966%5En%29

We want to know when the number of cars will be 58 million:

80%280.966%5En%29=58
0.966%5En=58%2F80

The quickest way to get an answer is by graphing on a graphing calculator. However, since the topic you chose is logarithms, we should get the answer that way.

log%28%280.966%5En%29%29=log%28%2858%2F80%29%29
n%2Alog%28%280.966%29%29=log%28%2858%2F80%29%29
n=log%28%2858%2F80%29%29%2Flog%28%280.966%29%29

We still need to get the answer using a calculator; but we did use logarithms to solve the problem.

I leave it to you to do the calculation and round the answer as directed.