Question

Paulina’s father pays her $20 per month for doing chores. In April, she makes a deal with him. Rather than paying her $20, he can pay her 1¢ on the first day of the month, 2¢ on the second, 4¢ on the third, and continue each day by doubling the amount he paid on the previous day. Use the properties of exponents to write expressions for the first 5 days of the month. The, explain if Paulina will make more or less than $20 per month using this pattern.

Answer 1

Answer:

Step-by-step explanation:

This is a geometric sequence with first element 1 and common ratio 2:

a(n) = 1*2^(n - 1)

Thus, a(1) = 1

a(2) = 2^(2 - 1) = 2

a(3) = 2^(3 - 1) = 4

a(4) = 2 ^( 4 - 1) = 2^ 3 = 8

a(5) = 2^(5  -1) = 2^ 4 = 16

One month is approximately 30 days.  Therefore,

a(30) = 2^ (30 - 1) = 2^29 = 536870912

Using this pattern, Paulina will "make" $536870.12 vs $20 via Paulina's father's plan.