Question

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32. Answer the questions about each type of relationship described below. ​

Answer 1

#a

Use geometric progression formula

• y=ar^{n-1}

Here

• r=2

First term =2(20)=40

• a=40

Equation

`\\ \rm\Rrightarrow y=40(2)^(n-1)`

After a year

`\\ \rm\Rrightarrow y=40(2)^(11)`

`\\ \rm\Rrightarrow y=40(2048)`

`\\ \rm\Rrightarrow y=\$81920`

#b

It's arithmetic as common difference is 50

`\\ \rm\Rrightarrow a_n=a+(n-1)d`

Equation

• First term =30+50=80

`\\ \rm\Rrightarrow a_n=80+(n-1)50`

After a year

`\\ \rm\Rrightarrow a_(12)=80+11(50)`

`\\ \rm\Rrightarrow 80+550`

`\\ \rm\Rrightarrow \$630`

Answer 2

PART (A):

As the total amount increases double each month. It is a geometric sequence equation. Fill the table.

Geometric Sequence: y = a(r)ˣ⁻¹

Here given:
First term (a) = 40
Common Difference (d) = 2

Equation: y = 40(2)ˣ⁻¹

After 1 year: y = 40(2)¹²⁻¹ = $81920

`\rule{300}{1}`

PART (B):

As the amount increases by $50 each month. It is a arithmetic or linear sequence.

Linear Equation: y = mx + b

Here given:
slope (m) = 50
starting (b) = 30

Equation: y = 50x + 30

After 1 year: y = 50(12) + 30 = 630