Salma just started a running plan where she runs 16 miles the first week and then increases the number of miles she runs by 5% each week. If she keeps up this plan for 6 weeks, how many total miles would Salma have run, to the nearest whole number? Answer:

Question

Salma just started a running plan where she runs 16 miles the first week and then increases the number of miles she runs by  5% each week. If she keeps up this plan for 6 weeks, how many total miles would Salma have run, to the nearest whole number? Answer:

Bytelearn · Accepted Answer

Identify Initial Amount: Identify the initial amount of miles Salma runs and the weekly percentage increase. Salma runs 16 miles the first week and increases her running distance by 5% each week. Initial miles (a) = 16 Percentage increase (r) = 5% or 0.05Calculate Total Miles: Calculate the total miles run for each week using the formula for the total distance after a percentage increase: Total miles for week n = Initial miles * (1 + r)^(n-1), where n is the week number. Week 1: 16 * (1 + 0.05)^(1-1) = 16 * (1 + 0.05)^0 = 16 * 1 = 16 Week 2: 16 * (1 + 0.05)^(2-1) = 16 * (1 + 0.05)^1 = 16 * 1.05 = 16.8 Week 3: 16 * (1 + 0.05)^(3-1) = 16 * (1 + 0.05)^2 ≈ 16 * 1.1025 ≈ 17.64 Week 4: 16 * (1 + 0.05)^(4-1) = 16 * (1 + 0.05)^3 ≈ 16 * 1.157625 ≈ 18.52 Week 5: 16 * (1 + 0.05)^(5-1) = 16 * (1 + 0.05)^4 ≈ 16 * 1.21550625 ≈ 19.44 Week 6: 16 * (1 + 0.05)^(6-1) = 16 * (1 + 0.05)^5 ≈ 16 * 1.2767813 ≈ 20.41Add Cumulative Distance: Add the total miles run each week to find the cumulative distance run over the 6 weeks. Total miles = Week 1 + Week 2 + Week 3 + Week 4 + Week 5 + Week 6 Total miles ≈ 16 + 16.8 + 17.64 + 18.52 + 19.44 + 20.41 ≈ 108.81Round Total Miles: Round the total miles to the nearest whole number as the question prompt asks for the answer to be rounded. Total miles rounded = 109 (to the nearest whole number)

Salma just started a running plan where she runs $16$ miles the first week and then increases the number of miles she runs by $5 \%$ each week. If she keeps up this plan for $6$ weeks, how many total miles would Salma have run, to the nearest whole number? $\newline$ Answer:

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Salma just started a running plan where she runs 161616 miles the first week and then increases the number of miles she runs by 5% 5 \% 5% each week. If she keeps up this plan for 666 weeks, how many total miles would Salma have run, to the nearest whole number?\newlineAnswer:

Salma just started a running plan where she runs $16$ miles the first week and then increases the number of miles she runs by $5 \%$ each week. If she keeps up this plan for $6$ weeks, how many total miles would Salma have run, to the nearest whole number? $\newline$ Answer: