Answer:
To solve the problem, we can use a formula to calculate the number of calories burned by Cindy each week, and then sum up the results for all four weeks.
Let C be the number of calories burned by Cindy in the first week (C = 2000 in this case), and let r be the weekly increase factor (r = 1.1, or 10% more per week). Then the number of calories burned by Cindy in week n can be calculated using the formula:
C_n = C * r^(n-1)
where n is the week number (starting from 1). For example, C_1 = C = 2000, C_2 = C * r = 2200, C_3 = C * r^2 = 2420, and so on.
To find the total number of calories burned by Cindy in all four weeks, we can sum up the values of C_1, C_2, C_3, and C_4:
Total calories = C_1 + C_2 + C_3 + C_4
= C + Cr + Cr^2 + Cr^3
= 2000 + 20001.1 + 20001.1^2 + 20001.1^3
= 2000 + 2200 + 2420 + 2662
= 9282
Therefore, Cindy will burn a total of 9,282 calories in all four weeks of following the exercise plan.
Explanation: