More Payment Options with Carl and Bernhard
Carl and Bernhard are back (remember them from the Exponential and Log Functions Target B investigation?). This time Carl has a much trickier payment option for Bernhard to consider for his summer job.
Carl says to Bernhard:
The devil made a proposition to Daniel Webster. The devil proposed to pay Daniel for services in the following way:
On the first day, I will pay you \(\$1000\) early in the morning. At the end of the first day, you must pay me a commission of \(\$100\); so, your net salary that day is \(\$900\). At the start of the second day, I will double your amount left at the end of the previous day. So, at the beginning of the second day, I will pay you \(\$1800\); but at the end of the second day, you must double the amount that you pay me to \(\$200\). Will you work for me for a month?
Practice Questions
1) After reading Carl’s proposal to Bernhard, would you work for Carl for a month?
2) Complete the following table to help you analyze this option further.
Carl and Bernhard are back (remember them from the Exponential and Log Functions Target B investigation?). This time Carl has a much trickier payment option for Bernhard to consider for his summer job.
Carl says to Bernhard:
The devil made a proposition to Daniel Webster. The devil proposed to pay Daniel for services in the following way:
On the first day, I will pay you \(\$1000\) early in the morning. At the end of the first day, you must pay me a commission of \(\$100\); so, your net salary that day is \(\$900\). At the start of the second day, I will double your amount left at the end of the previous day. So, at the beginning of the second day, I will pay you \(\$1800\); but at the end of the second day, you must double the amount that you pay me to \(\$200\). Will you work for me for a month?
Practice Questions
1) After reading Carl’s proposal to Bernhard, would you work for Carl for a month?
2) Complete the following table to help you analyze this option further.
3) Does the completed table change your decision at all?
4) If given the choice, how many days would you choose to work for Carl for? Why?
Extra Challenge
Plot the data for Bernhard’s salary and plot the data for Carl’s commission, what type of shape do each of the data plots make?
Now plot Bernhard’s net salary.
Comment on how each of the plots reveal the same information about how you should make your decision in question 1.
Adapted from illuminations.nctm.org