Final answer:
Annie will be paid 163.84 on the 15th week, as her payment doubles each week starting from $0.01, representing a geometric sequence with a common ratio of 2.
Step-by-step explanation:
To determine how much money Annie will be paid on the 15th week of washing the car, we need to understand that the amount she is paid each week is doubling. This scenario is described by a geometric sequence, where each term after the first is found by multiplying the previous term by a constant called the common ratio. In Annie's case, the first term (the amount she gets paid in the first week) is 0.01, and the common ratio (the factor by which her payment increases each week) is 2.
The formula for the n-th term of a geometric sequence is an = a1 × r(n-1), where:
- an is the n-th term of the sequence,
- a1 is the first term of the sequence,
- r is the common ratio,
- n is the term number.
Therefore, to find out the amount on the 15th week, we substitute the relevant numbers into the formula:
a15 = 0.01 × 2(15-1)
a15 = 0.01 × 214
a15 = 0.01 × 16384
a15 = $163.84
So, Annie will be paid 163.84 on the 15th week.