Question

Imagine you are four years old. A rich aunt wants to provide for your future. She hasoffered to do one of two things.Option 1: She would give you $1000.50 a year until you are twenty-one.Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amounteach year until you were 21.g. Explain what information you would need to know to determine the initial value in eachaccount/option 2. If it is helpful, come up with an example to show how to find it.

Answer 1

Data

Option 1

• $1000.50 per year until you are 21.

Option 2

• $1 this year, $2 next year, and so on, doubling the amount until 21.

Procedure

• Option 1

`y=1000.50\cdot x`

• Option 2

`y=\mleft(2\mright)^x`

Based on these equations, we would need to know the year that she would start giving us money and if the account had some money previously, as it would be added as a constant.

For example, if we had already $800, then we would have to add as follows:

`y=(2)^x+800`

Answer: we would have to know if the account had some money previously.