what is the answer to this math question?

Question

In an attempt to discredit the President, a member of the opposite political party wishes to start a scandalous rumor about him. He plans to tell people this rumor one week before election day and wants the entire population of the United States (that's 250,000,000 people!) to know the rumor. He needs to figure out how many people he should tell (and they each will tell the same number of people) so that everyone will have heard the rumor by the seventh day.


(b) Find the number of people the evil politician needs to tell so everyone in the United States will have heard the rumor by the seventh day. Remember: each person needs to tell the same number of people.

Answer 1

He tells N people each ofwhom tells N people the next day & each of them tell N people the day after that. the total will be N^7
so N^7=250,000,000
N=250,000,000^(1/7)=15.83 or 16 people.

Day 1: 16 people
Day 2: 16^2=256
Day 3: 16^3=4096
Day 4: 16^4=65536
Day 5: 16^5=1,045,576
Day 6: 16^6=16,777,216
Day 7: 16^7=268,435,456

Answer 2

We need to know how long it takes for one person to tell the rumor to the next person. Assuming that all this happens once a day, then you have n^7 = 250,000,000, where n is the number of people the President has to tell. To solve for n, take the seventh root of 250,000,000.

250,000,000^(1/7) = 15.83, so the President has to tell 16 people.