Task: Table-QA (source dataset: FinQA)

Task: 
You are given a table containing structured data and a natural language question referring to the table. Your goal is to analyze the table and provide an accurate and concise answer based on the given data.

Instructions:
1. Understand the Table: Examine the structure, headers, and data in the table. Identify relevant columns and rows related to the question.
2. Interpret the Question: Determine whether the question requires direct retrieval, aggregation, comparison, sorting, filtering, or inference.
3. Extract the Answer: Use logical reasoning and numerical operations (if necessary) to derive the correct response from the table.
4. Format the Answer: No explanation, return the answer in a structured JSON format: {"answer": <answer>}. If the question cannot be answered due to missing or ambiguous data, return a JSON response with {"answer": null}.

Table:
| Unnamed: 0                   | 2012           | 2011           | 2010           |
|:-----------------------------|:---------------|:---------------|:---------------|
| balance at beginning of year | $ 48.1         | $ 50.9         | $ 55.2         |
| additions charged to expense | 29.7           | 21.0           | 23.6           |
| accounts written-off         | -32.5 ( 32.5 ) | -23.8 ( 23.8 ) | -27.9 ( 27.9 ) |
| balance at end of year       | $ 45.3         | $ 48.1         | $ 50.9         |

Question:
what was the change in the allowance for doubtful accounts in 2012


pre_text: republic services , inc .
notes to consolidated financial statements 2014 ( continued ) high quality financial institutions .
such balances may be in excess of fdic insured limits .
to manage the related credit exposure , we continually monitor the credit worthiness of the financial institutions where we have deposits .
concentrations of credit risk with respect to trade accounts receivable are limited due to the wide variety of customers and markets in which we provide services , as well as the dispersion of our operations across many geographic areas .
we provide services to commercial , industrial , municipal and residential customers in the united states and puerto rico .
we perform ongoing credit evaluations of our customers , but do not require collateral to support customer receivables .
we establish an allowance for doubtful accounts based on various factors including the credit risk of specific customers , age of receivables outstanding , historical trends , economic conditions and other information .
no customer exceeded 5% ( 5 % ) of our outstanding accounts receivable balance at december 31 , 2012 and 2011 .
accounts receivable , net of allowance for doubtful accounts accounts receivable represent receivables from customers for collection , transfer , recycling , disposal and other services .
our receivables are recorded when billed or when the related revenue is earned , if earlier , and represent claims against third parties that will be settled in cash .
the carrying value of our receivables , net of the allowance for doubtful accounts , represents their estimated net realizable value .
provisions for doubtful accounts are evaluated on a monthly basis and are recorded based on our historical collection experience , the age of the receivables , specific customer information and economic conditions .
we also review outstanding balances on an account-specific basis .
in general , reserves are provided for accounts receivable in excess of ninety days old .
past due receivable balances are written-off when our collection efforts have been unsuccessful in collecting amounts the following table reflects the activity in our allowance for doubtful accounts for the years ended december 31 , 2012 , 2011 and 2010: .
post_text: restricted cash and marketable securities as of december 31 , 2012 , we had $ 164.2 million of restricted cash and marketable securities .
we obtain funds through the issuance of tax-exempt bonds for the purpose of financing qualifying expenditures at our landfills , transfer stations , collection and recycling centers .
the funds are deposited directly into trust accounts by the bonding authorities at the time of issuance .
as the use of these funds is contractually restricted , and we do not have the ability to use these funds for general operating purposes , they are classified as restricted cash and marketable securities in our consolidated balance sheets .
in the normal course of business , we may be required to provide financial assurance to governmental agencies and a variety of other entities in connection with municipal residential collection contracts , closure or post- closure of landfills , environmental remediation , environmental permits , and business licenses and permits as a financial guarantee of our performance .
at several of our landfills , we satisfy financial assurance requirements by depositing cash into restricted trust funds or escrow accounts. .
label: -2.8
qa: answer: -2.8
explanation: the allowance for doubtful accounts change by 2.81 in 2012
ann_table_rows: 1
4
steps: op: minus1-1
arg1: 45.3
arg2: 48.1
res: -2.8
program: subtract(45.3, 48.1)
gold_inds: table_1: the balance at beginning of year of 2012 is $ 48.1 ; the balance at beginning of year of 2011 is $ 50.9 ; the balance at beginning of year of 2010 is $ 55.2 ;
table_4: the balance at end of year of 2012 is $ 45.3 ; the balance at end of year of 2011 is $ 48.1 ; the balance at end of year of 2010 is $ 50.9 ;
exe_ans: -2.8
tfidftopn: text_9: accounts receivable , net of allowance for doubtful accounts accounts receivable represent receivables from customers for collection , transfer , recycling , disposal and other services .
program_re: subtract(45.3, 48.1)
model_input: table_1
the balance at beginning of year of 2012 is $ 48.1 ; the balance at beginning of year of 2011 is $ 50.9 ; the balance at beginning of year of 2010 is $ 55.2 ;
table_4
the balance at end of year of 2012 is $ 45.3 ; the balance at end of year of 2011 is $ 48.1 ; the balance at end of year of 2010 is $ 50.9 ;
text_16
restricted cash and marketable securities as of december 31 , 2012 , we had $ 164.2 million of restricted cash and marketable securities .