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

Select The Recursive And Explicit Formula For The Arnold Family 2 Answer class=

Sagot :

ANSWER:

[tex]\begin{gathered} A\left(n\right)=a_{n-1}\times 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^{n-1} \end{gathered}[/tex]

STEP-BY-STEP 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:

[tex]A(n)=0.05\cdot(2)^{n-1}[/tex]

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:

[tex]A(n)=a_{n-1}\times2[/tex]

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

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