Consumers in a certain state can choose between three long-distance telephone services: gtt, ncj, and dash. aggressive marketing by all three companies results in continual shift of customers among the three services. each year, gtt loses 30% of its customers to ncj and 15% to dash, ncj loses 10% of its customers to gtt and 5% to dash, and dash loses 30% of its customers to gtt and 30% to ncj. assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?

40 minutes

step-by-step explanation:

add the time and multiply by 2

im pretty sure its

(8,15)

step-by-step explanation:

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