You are running a small business. At the beginning of the month you have $1000. At the end of the first week you have revenues of $2200 and expenses of $1000 for that week. In the second week your revenues are $2000 and your expenses are $700. In the third week your revenues are $2100 and your expenses are $1100. In the fourth week, your revenues are $2200 and your expenses are $3000 (they are higher as you need to pay the rent). You have a checking account earning 1% annually compounded weekly. a) How much money do you have at the end of the four weeks? b) What is the minimum balance of the account over those four weeks? Does it ever drop below $1000?

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kitttimothy55

09.08.2020

Mathematics

$f(x)=|-2x+1|\qquad \qquad \stackrel{domain}{\{-2~~,~~1~~,~~\frac{2}{3}\}} \\\\[-0.35em] ~\dotfill\\\\ f(-2)=|-2(-2)+1|\implies f(-2)=|4+1|\implies f(-2)=\boxed{5} \\\\\\ f(1)=|-2(1)+1|\implies f(1)=|-2+1| \\\\\\ \qquad f(1)=|-1|\implies f(1)=\boxed{1}$

$f\left( \frac{2}{3} \right)=\left|-2\left( \frac{2}{3} \right)+1\right|\implies f\left( \frac{2}{3} \right)=\left|-\frac{4}{3}+1\right|\implies f\left( \frac{2}{3} \right)=\left|\frac{-4+3}{3}\right| \\\\\\ \qquad \qquad f\left( \frac{2}{3} \right)=\left|-\frac{1}{3}\right|\implies f\left( \frac{2}{3} \right)=\boxed{\frac{1}{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{range}{\{5~~,~~1~~,~~\frac{1}{3}\}}~\hfill$

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