Juana’s dad gave her an exponentially increasing allowance as an experiment. On the first day, he gave her 1¢. On the second day he doubled it and gave her 2¢, and on the third day, he doubled that and gave her 4¢. He kept doubling the previous day’s amount for a total of 10 days. How much did he give her on the tenth day?

Question

richyw · Answer

Let $a_n$ be the amount of allowance (in cents) given on day number n. Then,
$$a_n= 2^{n-1}$$Is a function that satisfies this. For example on the first day you would plug in $$a_1=2^{1-1}=1$$or on day 3 you would plug in $$a_3=2^{3-1}=2^2=4$$