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.
Step-by-step 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!!!
were incorrect, it means that 
were correct