Your parents ask you to choose between two offers for an allowance. The first offer is to receive one penny on the first day, 2 penny’s on the second day, 4 pennies on the third day, 8 pennies on the fourth day and so on. (365 days). Second offer is to receive 10 dollars the first week, 20 dollars the second week, 30 dollars the third week, and so on, for the entire year (52 weeks). Which offer should you choose to make more money?

Answer:The penniesStep-by-step explanation:We can create a geometric equation for the pennies and an arithmetic equation for the dollars.The format for a geometric equation is [tex]y=a_1(\frac{1-r^n}{1-r} )[/tex]If we plug in the values we already know we should get the equation.[tex]y=2^x-1[/tex]Now we can plug in the number of days in a year for [tex]x[/tex] to find how much money we get.[tex]2^{365}=7.52*10^{109}[/tex]Which is basically 752 with 107 zeros following it. Then we can divide this number by 100 to find the number of dollars it is.We get 752 with 105 zeros following it.Now we can find the arithmetic equation for the dollars.We can see that 10 dollars is being added every time.Use the formula.[tex]a_n=a_1+m(n-1)[/tex]We can plug in.[tex]a_n=10+10(n-1)[/tex]Now we can substitute 52 for [tex]x[/tex] in the equation.[tex]a_{52}=10+10(52-1)[/tex][tex]a_{52}=10+510 \\ \\a_{52}=520[/tex]So you'll be getting 520 dollars at the end of the year, which is far less than the amount of money you get from the pennies.