The growing colony

Problem

Nobody on the Aurora colony, on a moon of Jupiter, counts as half a person. Every year new settlers arrive: pct % of the population at that moment, rounded down. And since some ship always shows up, if that comes out to 0, 1 settler arrives that year.

Write a function that takes start, pct and goal (whole numbers, with start and goal 1 or more and pct from 1 to 100) and returns how many years pass until the population is goal or more.

With 100, 10 and 150: 100 + 10 = 110, 110 + 11 = 121, 121 + 12 = 133 (10 % of 121 is 12.1, which becomes 12), 133 + 13 = 146 and 146 + 14 = 160: 5 years. With 10 people and 3 %, the count is 0.3, which becomes 0, so 1 arrives. If start is already goal or more, it is 0 years.

Examples

• The example

  100, 10, 150 → 5

• Doubles every year

  1, 100, 1024 → 10

• Lands exactly on the goal

  30, 10, 60 → 8

• Rounding down adds up

  200, 7, 1000 → 25

• At least one always arrives

  10, 3, 15 → 5

Besides these, the challenge has hidden tests that are revealed when you submit your solution.

You start with this

def years_to_goal(start, pct, goal):
    pass

function yearsToGoal(start, pct, goal) {
}