Answer:
a) 6,880
b) 4,059
c) Check Explanation
The number of expected votes for candidate A increases only in the first 3 weeks of mudslinging. The rate of weekly increase in those 3 weeks, is provided in the explanation. The number changes weekly for those 3 weeks with an average increase of 101 new votes per week.
Explanation:
a. If the election were held today, how many people would vote?
b. How many of those would vote for candidate A?
c. How rapidly is the number of votes that candidate A will receive increasing at the moment?
There are 16,000 registered voters, 43% of whom are planning to vote, with 59% planning to vote for candidate A.
a) Number of registered voters planning to vote = 43% × 16000 = 6880
b) Number of registered voters that will vote and vote for candidate A
= 59% of registered voters planning to vote
= 59% × 6880 = 4059.2 ≈ 4059 people
c) Polls show that the percentage of people who plan to vote is increasing by 5 percentage points per week, and the percentage who will vote for candidate A is declining by 4 percentage points per week.
Since, the 'moment' isn't specified, we will check how much the number is increasing for the first 4 weeks after the mudslinging by candidate B began
Normally, 43% of registered voters want to vote, but now it is increasing at a rate of 5% per week. So, the percentage of registered voters that want to vote is now
43% + 5x% (where x = number of weeks after the mudslinging by candidate B started)
And the percentage of voting, registered voters that want to vote for candidate A is now (59% - 4x%)
After a week, percentage of registered voters that will vote = 48%
Number of registered voters that will vote = 48% × 16000 = 7680
percentage of voting, registered voters that want to vote for candidate A = 55%
Number of voting, registered voters that want to vote for candidate A = 55% × 7680 = 4224
Difference between the initial number of expected votes for candidate A between the beginning of the mudslinging and end of week 1
= 4224 - 4059 = 165
After week 2,
percentage of registered voters that will vote = 53%
Number of registered voters that will vote = 53% × 16000 = 8480
percentage of voting, registered voters that want to vote for candidate A = 51%
Number of voting, registered voters that want to vote for candidate A = 51% × 8480 = 4324.8 = 4325
Difference between the number of expected votes for candidate A between week 1 and week 2
= 4325 - 4224 = 101
After week 3,
percentage of registered voters that will vote = 58%
Number of registered voters that will vote = 58% × 16000 = 9280
percentage of voting, registered voters that want to vote for candidate A = 47%
Number of voting, registered voters that want to vote for candidate A = 47% × 9280 = 4361.6 = 4362
Difference between the number of expected votes for candidate A between week 2 and week 3
= 4362 - 4325 = 37
After week 4,
percentage of registered voters that will vote = 63%
Number of registered voters that will vote = 63% × 16000 = 10,080
percentage of voting, registered voters that want to vote for candidate A = 43%
Number of voting, registered voters that want to vote for candidate A = 43% × 10080 = 4334
Difference between the number of expected votes for candidate A between week 3 and week 4
= 4334 - 4362 = -28
The number of expected votes for candidate A begins to decline after the 4th week of mudslinging.
So, the required 'moment' should be within the first 3 weeks of mudslinging. And the rate of increase weekly is provided above with an average increase of 101 new voters per week.
Hope this Helps!!!