Ok if someone can help me understand I greatly appreciated. I want to know how this is the answer the numbers in table I know answer is day 6 but the pattern?. I got it wrong in my exam. The teacher explained it to me but I still don't get it.

Question

On July 5,in the area around center village,there was great excitement. Six different people reported the police that they had seen bigfoot,the large hairy creature sometimes seen but never captured. The next day the police received twice as many calls as the day before. After they got a total of more than 300 calls, the police took the phone off the hook!on what day did the police receive their 300 call?

Answer:(table with day/#of calls/total.

Day 1:6 calls / total 6
Day 2:12 calls /total 18
Day 3:24 calls /total 42
Day 4:48 calls /total 90
Day 5:96 calls/total 186
Day 6:192 calls/total 378

Answer 1

I'll try to explain it even though I don't understand your confusion.

Alright so on
Day One: There was 6 reporting calls
Day Two: Doubled from 6 to 12
- (Total of 18 calls now)

Day Three: Doubled from 12 to 24
- (Total of 42 calls now)

Day Four: Doubled from 24 to 48
- (Total of 90 calls now)

Day Five: Doubled from 48 to 96
- (Total of 186 calls now)

Day Six: Doubled from 96 to 192
- (Total of 378 calls now, meaning that the total was larger then 300 calls on day six so the phone was taken off on this day)

The pattern is that the amount of phone calls is doubled from the previous days number of calls.
Hope this solves your confusion :)

Answer 2

so you are just adding
6 + 12 + 24 + 48 + ... until you get 300

This is the sum of a geometric series with
a = 6, and r = 2
sum(n) = a(r^n -1)/(r-1)
300 = 6(2^n -1)/(2-1)
50 = 2^n - 1
2^n = 51
since n has to be a whole number, we can just take a stab at it
2^5 = 32
2^6 = 64 , but want 51 , so after 6 days they received more than 300 calls

sum(5) = 6(2^5 - 1)/1 = 186
sum(6) = 6(2^6 - 1) = 378 > 300