The number of exercises on Khan academy has increased rapidly since it began in 2006. The relationship between the elapsed time, t, in years, since Khan academy began, and the total number of its exercises, E_("year ")(t), is modeled by the following function: E_("year ")(t)=100*(1.7)^(t) Complete the following sentence about the monthly rate of change in the number of exercises. Round your answer to two decimal places. Every month, the number of exercises increases by a factor of

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The number of exercises on Khan academy has increased rapidly since it began in 2006. The relationship between the elapsed time,  t, in years, since Khan academy began, and the total number of its exercises,  E_("year ")(t), is modeled by the following function:  E_("year ")(t)=100*(1.7)^(t) Complete the following sentence about the monthly rate of change in the number of exercises. Round your answer to two decimal places. Every month, the number of exercises increases by a factor of

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Understand the function: Understand the given function. The function E_(＂year ＂)(t)=100*(1.7)^(t) represents the total number of exercises E as a function of time t in years since Khan Academy began. The base of the exponent, 1.7, represents the annual growth factor.Convert to monthly growth factor: Convert the annual growth factor to a monthly growth factor. Since there are 12 months in a year, we need to find the 12th root of 1.7 to determine the monthly growth factor. Monthly growth factor = (1.7)^(1/12)Calculate monthly growth factor: Calculate the monthly growth factor. Using a calculator, we find the 12th root of 1.7. (1.7)^(1/12) ≈ 1.04589Round monthly growth factor: Round the monthly growth factor to two decimal places. Rounded monthly growth factor ≈ 1.05Complete the sentence: Complete the sentence with the calculated monthly growth factor. Every month, the number of exercises increases by a factor of approximately 1.05.

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