11 Jill has 3 daughters and no sons. They are generation 1 of Jill's descendants.
Each of her daughters has 3 daughters and no sons. Jill's 9 granddaughters are generation 2 of her descendants. Each of her granddaughters has 3 daughters and no sons; they are descendant generation 3.
Jill decides to investigate what would happen if this pattern continues, with each descendant having 3 daughters and no sons.
- How many of Jill's descendants would there be in generation 8 ?
- How many of Jill's descendants would there be altogether in the first 15 generations?
- After \(n\) generations, Jill would have over a million descendants altogether. Show that \(n\) satisfies the inequality
$$n > \frac { \log _ { 10 } 2000003 } { \log _ { 10 } 3 } - 1 .$$
Hence find the least possible value of \(n\).
- How many fewer descendants would Jill have altogether in 15 generations if instead of having 3 daughters, she and each subsequent descendant has 2 daughters?
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