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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.

Part A: Write a recursive and explicit formula for each option.


The Arnold Family:


The Gainey Family:

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Answer:

Kindly check Explanation

Step-by-step explanation:

The Arnold family :

Recursive formula ;

A1 = $1

A2 = $1 + 2($1) = $3

A3 = $3 + 2($3) = $9

An = An-1 + 2(An-1)

Where n = day of the month

Explicit formula;

y = a(b)^c

Where :

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c

Gainey's Family:

Recursive formula:

A1 = $10

A2 = A1 + $10 = $10 + $10 = $20

A3 = A2 + $10 = $20 + $10 =$30

An = An-1 + $10

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

Formula saving for The Arnold Family and The Gainey Family are 0.05 × 2⁽ⁿ⁻¹⁾ and  10 + 10(n-1)

Recursive and explicit formula:

Recursive Amount saved by Arnold Family = Amount save on first day × 2⁽ⁿ⁻¹⁾

Amount saved by Arnold Family = (1/20) × 2⁽ⁿ⁻¹⁾

Amount saved by Arnold Family = 0.05 × 2⁽ⁿ⁻¹⁾

Recursive Amount saved by Gainey Family = 10 + 10(n-1)

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