At the end of 2010, a gaming website had 100,000 users. The number of users grew at a rate of \( 40 \% \) per year until the end of 2015 . How many more users joined the website between the end of 2013 and the end of 2015 ?

To find out how many more users joined the website between the end of 2013 and the end of 2015, we need to calculate the number of users at the end of 2013 and the end of 2015, and then find the difference between these two numbers. Given: - Initial number of users at the end of 2010 = 100,000 - Growth rate = 40% per year Let's calculate the number of users at the end of 2013 and the end of 2015: 1. Calculate the number of users at the end of 2013: - Number of users at the end of 2010 = 100,000 - Growth rate = 40% per year - Number of years from 2010 to 2013 = 3 years 2. Calculate the number of users at the end of 2015: - Number of users at the end of 2013 (calculated above) - Growth rate = 40% per year - Number of years from 2013 to 2015 = 2 years Let's calculate the number of users at the end of 2013 and the end of 2015. Calculate the value by following steps: - step0: Calculate: \(100000\left(1+0.4\right)^{3}\) - step1: Add the numbers: \(100000\times 1.4^{3}\) - step2: Convert the expressions: \(100000\left(\frac{7}{5}\right)^{3}\) - step3: Evaluate the power: \(100000\times \frac{343}{125}\) - step4: Multiply: \(274400\) Calculate or simplify the expression \( 274400 * (1 + 0.4)^2 \). Calculate the value by following steps: - step0: Calculate: \(274400\left(1+0.4\right)^{2}\) - step1: Add the numbers: \(274400\times 1.4^{2}\) - step2: Convert the expressions: \(274400\left(\frac{7}{5}\right)^{2}\) - step3: Evaluate the power: \(274400\times \frac{49}{25}\) - step4: Multiply: \(537824\) The number of users at the end of 2013 is 274,400, and the number of users at the end of 2015 is 537,824. Now, let's find the difference in the number of users between the end of 2013 and the end of 2015. Calculate the value by following steps: - step0: Calculate: \(537824-274400\) - step1: Subtract the numbers: \(263424\) The difference in the number of users between the end of 2013 and the end of 2015 is 263,424.