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: .

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)
(23.8)
(27.9)
Balance at end of year
$45.3
$48.1
$50.9

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. .

Question: Analyse this data from a financial earnings document. what was the percentage change in the additions charged to expense from 2011 to 2012 as part of the allowance for doubtful accounts
Choices:
0.12381
-2.32857
0.36864
0.41429
0.29293
Correct choice index: 3