Investigation Solutions
1. If Bernhard works \(14\) days, he will make \(\$700\) with option 1 and \(\$163.84\) with option 2.
2. If Bernhard plans to work more than \(16\) days he should choose option 2.
3. Option 1: \(30(50)=1500\), Option 2: \(0.01(2)^{30}=10,737,418.24\) Bernhard should choose option 2 if he can work for \(30\) days.
4.If Bernhard plans to work for a short time, he should choose option 1, but eventually option 2 ends up yielding much more money. He needs to consider how long he is going to work.
1. If Bernhard works \(14\) days, he will make \(\$700\) with option 1 and \(\$163.84\) with option 2.
2. If Bernhard plans to work more than \(16\) days he should choose option 2.
3. Option 1: \(30(50)=1500\), Option 2: \(0.01(2)^{30}=10,737,418.24\) Bernhard should choose option 2 if he can work for \(30\) days.
4.If Bernhard plans to work for a short time, he should choose option 1, but eventually option 2 ends up yielding much more money. He needs to consider how long he is going to work.
5.Around \(16.316\) days is the point where the two options pay the same. Anything before this, option 1 pays more, anything after this option 2 pays more.
Bonus: \(\sum\limits_{i=0}^{14} 0.01(2)^{i}=327.66\). We have much more after \(14\) days with option 3 than option 2, but option 1 still yields more.
Bonus: \(\sum\limits_{i=0}^{14} 0.01(2)^{i}=327.66\). We have much more after \(14\) days with option 3 than option 2, but option 1 still yields more.