Question

Andrew just started a running plan where he runs 12 miles the first week and then increases the number of miles he runs by 5% each week. If he keeps up this plan for 10 weeks, how many total miles would Andrew have run, to the nearest whole number?

Answer 1

To find how many total miles Andrew would have run after 10 weeks with a 5% increase each week, we use the sum of geometric series formula, with the first term of 12 miles, a common ratio of 1.05, and 10 terms.

Step-by-step explanation:

To calculate the total number of miles Andrew would have run after 10 weeks with a 5% increase each week starting at 12 miles, we need to use a geometric series. The first week's mileage is 12 miles, and each week, the mileage increases by 5%, which means we multiply the previous week's mileage by 1.05 to get the next week's mileage.

The total mileage run after n weeks can be found using the formula for the sum of a geometric series: S = a(1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

In Andrew's case, a = 12, r = 1.05, and n = 10. Plugging these values into the formula gives us the total distance:

S = 12(1 - 1.05^10) / (1 - 1.05)

=150.93

Answer 2

18 miles.

Step-by-step explanation:

You start with 12 miles and then you first need to figure out what 5% of that is by doing the equation x/12 = 5/100 and you will then get .6. Then you multiply that number by 10 (one for each week) getting 6. Then you add the 6 to your starting total to get 18.