what was the percent of the change in the weighted average risk-free interest rate
american tower corporation and subsidiaries notes to consolidated financial statements assessments in each of the tax jurisdictions resulting from these examinations . the company believes that adequate provisions have been made for income taxes for all periods through december 31 , 2010 . 12 . stock-based compensation the company recognized stock-based compensation of $ 52.6 million , $ 60.7 million and $ 54.8 million for the years ended december 31 , 2010 , 2009 and 2008 , respectively . stock-based compensation for the year ended december 31 , 2009 included $ 6.9 million related to the modification of the vesting and exercise terms for certain employee 2019s equity awards . the company did not capitalize any stock-based compensation during the years ended december 31 , 2010 and 2009 . summary of stock-based compensation plans 2014the company maintains equity incentive plans that provide for the grant of stock-based awards to its directors , officers and employees . under the 2007 equity incentive plan ( 201c2007 plan 201d ) , which provides for the grant of non-qualified and incentive stock options , as well as restricted stock units , restricted stock and other stock-based awards , exercise prices in the case of non-qualified and incentive stock options are not less than the fair market value of the underlying common stock on the date of grant . equity awards typically vest ratably over various periods , generally four years , and generally expire ten years from the date of grant . stock options 2014as of december 31 , 2010 , the company had the ability to grant stock-based awards with respect to an aggregate of 22.0 million shares of common stock under the 2007 plan . the fair value of each option grant is estimated on the date of grant using the black-scholes option pricing model based on the assumptions noted in the table below . the risk-free treasury rate is based on the u.s . treasury yield in effect at the accounting measurement date . the expected life ( estimated period of time outstanding ) was estimated using the vesting term and historical exercise behavior of company employees . the expected volatility was based on historical volatility for a period equal to the expected life of the stock options . key assumptions used to apply this pricing model are as follows: .

|  | 2010 | 2009 | 2008 |
| :--- | :--- | :--- | :--- |
| Range of risk-free interest rate | 1.41% – 2.39% | 1.41% – 2.04% | 1.44% – 3.05% |
| Weighted average risk-free interest rate | 2.35% | 1.71% | 1.89% |
| Expected life of option grants | 4.60 years | 4.00 years | 4.00 years |
| Range of expected volatility of underlying stock price | 37.11% – 37.48% | 36.00% – 36.63% | 28.51% – 35.30% |
| Weighted average expected volatility of underlying stock price | 37.14% | 36.23% | 29.10% |
| Expected annual dividends | N/A | N/A | N/A |

the weighted average grant date fair value per share during the years ended december 31 , 2010 , 2009 and 2008 was $ 15.03 , $ 8.90 and $ 9.55 , respectively . the intrinsic value of stock options exercised during the years ended december 31 , 2010 , 2009 and 2008 was $ 62.7 million , $ 40.1 million and $ 99.1 million , respectively . as of december 31 , 2010 , total unrecognized compensation expense related to unvested stock options was approximately $ 27.7 million and is expected to be recognized over a weighted average period of approximately two years . the amount of cash received from the exercise of stock options was approximately $ 129.1 million during the year ended december 31 , 2010 . during the year ended december 31 , 2010 , the company realized approximately $ 0.3 million of state tax benefits from the exercise of stock options. .

risk_free_rate_2010 = 2.35
risk_free_rate_2009 = 1.71
percent_change = (risk_free_rate_2010 - risk_free_rate_2009) / risk_free_rate_2009
answer = percent_change * 100