After reading fantastic beasts and where to find them, your professor discovers that unicorns are equally likely to have 0, 1, 2, or 3 offspring. unfortunately, only one unicorn is left. that is, let (zn)∞ n=0 be a branching process that describes the population of unicorns at time n. the offspring distribution is uniformly distributed on {0, 1, 2, 3}, and z0 = 1. (a) find the probability that the population of unicorns will go extinct by the second generation. (b) find the probability that the population of unicorns goes extinct.

i got 10.28 but that rounds up to 10.3

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