On day 1, the penalty is $0.01. On day 2, the penalty is $.02. On day 3 the penalty was $.04, on day 4 the penalty was $.08. Doubling in amount each additional day late, what is the equation?

Question

Mathematics

Lexie Small

4 June, 16:42

On day 1, the penalty is $0.01. On day 2, the penalty is $.02. On day 3 the penalty was $.04, on day 4 the penalty was $.08. Doubling in amount each additional day late, what is the equation?

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Answers (1)

Know the Answer?

Kylee Dudley · Answer 1

a (n) = $0.01*2 (n - 1)

Step-by-step explanation:

Let a (n) represent the nth term of this geometric sequence. The common ratio is 2 (which comes from "doubling."

Then the desired formula is a (n) = $0.01*2 (n - 1).

Check: Day 1: a (1) = $0.01*2 (1 - 1) = $0.01

Day 2: a (2) = $0.01*2 (2 - 1) = $0.02

Day 3: a (3) = $0.01*2 (3 - 1) = $0.04

and so on

... which shows that this formula is valid