Question

Select the recursive and explicit formula for the Arnold family 2 answer

Answer 1

`\begin{gathered} A\left(n\right)=a_(n-1)* 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^(n-1) \end{gathered}`

Explanation:

We have that the Arnolds family are going to save a nickel on the first day of the month and then double the amount each day.

One nickel is equal to $0.05, therefore, we can make an recursive formula, it is a geometric sequence where the initial value is 0.05 and the ratio is equal to 2, because it doubles every day, therefore:

`A(n)=0.05\cdot(2)^(n-1)`

Now, from the above we can deduce the explicit formula, since the next value will be double the previous value, therefore, the explicit formula would be:

`A(n)=a_(n-1)*2`

Therefore, the correct answers are the 1st and 4th options.