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PLS HELP ASAP WILL GIVE BRAINLIEST AND 100 POINTS
A hiker on the Appalachian Trail planned to increase the distance covered by 20% each day. After 7 days, the total distance traveled is 51.664 miles.

Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)

Part B: What is the equation for Sn? Show all necessary math work. (3 points)

Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)

plsss help if you can im spending 100 points ://

Sagot :

waysidecosine

Part A: He started with 4 miles.

Explanation Part A:    51.664 = (x((1.2⁷)-1)) / 0.2


Part B: The equation is 51.664 = (x(1.2⁷)-1)/0.2

Explanation: n = 7 and on day 7 he traveled 51.664 so Sn = 51.664.

We get the second part of the equation because each day is increased by 20% so we have r = (1.2x) / x = 1.2

So our top half will be x multiplied by ((1.2)⁷-1) because it's the 7th day and we are increasing by 1.2x - 1.

Our bottom half is 1.2 - 1 which equals 0.2

Part C : 103.83 miles

Explanation: We now have x which is 4 so we plug x into the equation above and remove the 51.664. We also change the 1.2⁷ to 1.2¹⁰ because it's the 10th day not the 7th.

Our equation now looks like (4(1.2¹⁰)-1) / 0.2 which is equal to 103.83 miles.

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