Question

The Gaineys and the Arnolds are saving money for a trip to Utah to go snowboarding. The Arnolds are going to save a nickel on the first day of the month and then double the amount each day for a month. The Gaineys are going to start their savings by saving $10 on the first day and then $10 each day of the month.
Write a recursive and explicit formula for each option

Answer 1

Answer: see Explanation

Step-by-step explanation:

THE GAINEY'S:

Recursive Formula :

A1 = $10

An = An-1 + $10

A2 = $10 + $10 = $20

Where n = day of the month

Explicit formula :

y = a + b(c - 1)

WHERE:

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c

THE ARNOLD'S :

Recursive formula:

First day of the month (A1) = $10

An = 2(An-1)

A2 = 2(A1) = 2(10) = $20

A3 = 2(A2) = 2(20) =$40

Explicit formula:

y = a(b)^c

Where :

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c