Question

jobie starts with $325 in her piggy bank. each month she adds $10. which recursive function rule models the total amount in jobie’s piggy bank at the end of each month?\\(\boldsymbol{a_n = 325 \cdot a_{n-1}}\\) and \\(\boldsymbol{a_1 = 10}\\)\\(\boldsymbol{a_n = 10 \cdot a_{n-1}}\\) and \\(\boldsymbol{a_1 = 325}\\)\\(\boldsymbol{a_n = 10 + a_{n-1}}\\) and \\(\boldsymbol{a_1 = 325}\\)\\(\boldsymbol{a_n = 325 + a_{n-1}}\\) and \\(\boldsymbol{a_1 = 10}\\)

Explanation:

Step1: Analyze Initial Amount

Jobie starts with $325, so the first term \( a_1 = 325 \).

Step2: Analyze Monthly Addition

Each month she adds $10, so the amount at month \( n \) is the previous amount (\( a_{n - 1} \)) plus 10. Thus, the recursive formula is \( a_n = 10 + a_{n - 1} \) with \( a_1 = 325 \).

Answer:

\( a_n = 10 + a_{n - 1} \) and \( a_1 = 325 \) (the option with this description)