According to a local survey performed in January, 49% of people polled said they would reelect the town's mayor. However, the mayor's percentage of votes decreased 2% each month. The survey revealed that 19% of the people polled would vote for the challenger. The challenger's percentage of votes increased 3% each month. In what month will the percentage of people willing to vote for the challenger equal to that of the mayor? What percent will vote for the challenger in that month?
49*.98^t = 19*1.03^t
t = 19.08
so, the following August the polls will match.
To determine the month when the percentage of people willing to vote for the challenger equals that of the mayor, we can set up an equation and solve for the unknown variable, which is the number of months.
Let's assume "x" represents the number of months.
The starting percentage of people willing to reelect the mayor is 49%, and it decreases by 2% each month. So, the percentage of people willing to reelect the mayor after "x" months can be represented as:
49% - 2%x
The starting percentage of people willing to vote for the challenger is 19%, and it increases by 3% each month. So, the percentage of people willing to vote for the challenger after "x" months can be represented as:
19% + 3%x
To find the month when the percentages are equal, we can set up the equation:
49% - 2%x = 19% + 3%x
Let's solve this equation:
49% - 19% = 3%x + 2%x
30% = 5%x
30/5 = x
6 = x
Therefore, the percentage of people willing to vote for the challenger will be equal to that of the mayor in the 6th month.
To find the percentage of people willing to vote for the challenger in that month, substitute the value of "x" into the equation for the challenger's percentage:
19% + 3% * 6 = 19% + 18% = 37%
In the 6th month, 37% of people polled will vote for the challenger.