The number of full-time and part-time employees of an online retailer increased exponentially from 69 thousand in 2011 to 306.9 thousand in 2016. a) Let t=0 correspond to 2011 and t=5 correspond to 2016. Then t is the number of years after 2011. Use the data points (0,69) and (5,306.9) to find the exponential growth rate and fit an exponential growth function P(t)=P0ekt to the data, where P(t) is the number of employees, in thousands, t years after 2011. b) Use the function found in part (a) to estimate the number of employees in 2017. c) According to this model, when will there be one million employees? a) P(t)=?

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Caren · Accepted Answer

Step 1 Given the number of full time and part b time employees of an online retailer increased exponential from 69 thousand in 2011 to 306.9 thousand in 2016. Step 2 a) Given exponential equation p(t)=P0ekt (1) Given, when t=0,P(t)=68thousand Therefore P(0)=P0ek×0=68 ⇒P0=68 Also wen t=5,P(t)=306.6 thousand Then P(5)=P0e5k=306.6 ⇒68e5k=306.6 ⇒e5k=306.668 ⇒5k=ln⁡(306.668) ⇒k=15ln⁡(306.668)=0.301 Therefore P(t)=68e0.301t b) In this case t=(2017−2011)=6 Substituting t=6, we get number of employees in 2017 =68e0.301×6 =413.852 thousand c) Let us assume the population will be one million or 1000 thousand n years. Therefore 68×e0.301×n=1000 ⇒e0.301n=100068 ⇒0.301n=ln⁡(100068) ⇒n=10.301ln⁡(100068)=8.93 years ≈9 years. Therefore population will be one million employees 9 year after 2011 i.e. in the year 2020.

The number of full-time and part-time employees of an online retailer increased

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