Road rambler sells specialty running shoes and apparel through catalogs and the web. customers can phone in orders at any time day or night, 7 days a week. during the 4 a. m. to 8 a. m. shift, a single sales rep handles all calls. during this time, calls arrive at a rate of 14 per hour following a poisson distribution. it takes the sales rep an average of four minutes to process each call. the variability in service times is approximately exponentially distributed. all calls received while the sales rep is busy are placed in a queue.

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the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places