SOLUTION: Solve for x (round to the nearest hundredth): 200=400e^-0.0052x

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Question 1192941: Solve for x (round to the nearest hundredth):
200=400e^-0.0052x
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

200=400e%5E%28-0.0052x%29.........take natural log of both sides
ln%28200%29=ln%28400e%5E%28-0.0052x%29%29
ln%28200%29=ln%28400%29%2Bln%28e%5E%28-0.0052x%29%29
ln%282%2A10%5E2%29-ln%284%2A10%5E2%29=%28-0.0052x%29ln%28e%29
%28-0.0052x%29ln%28e%29=ln%282%29%2Bln%2810%5E2%29-%28ln%282%5E2%29%2Bln%2810%5E2%29%29.......ln%28e%29=1
-0.0052x=ln%282%29%2B2ln%2810%29-%282ln%282%29%2B2ln%2810%29%29
-0.0052x=ln%282%29%2B2ln%2810%29-2ln%282%29-2ln%2810%29......simplify
-0.0052x=-ln%282%29
x=-ln%282%29%2F-0.0052
x=ln%282%29%2F0.0052
x=133.2975347230664
x=133.30



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


You make a lot of extra unnecessary work by immediately taking logs of both sides, as the other tutor did. Make the work MUCH easier by first dividing both sides by 400.

200=400e%5E%28-0.0052x%29
e%5E%28-0.0052x%29=0.5

NOW take logs of both sides

-0.0052x=ln%280.5%29
x=ln%280.5%29%2F-0.0052 = 133.30 to 2 decimal places

ANSWER: 133.30