Erina runs 200 meters each day during the first week of her training. She plans to increase the distance she runs each week. Erina's training goal is
to run 150% of the distance she ran each day in the previous week. She will run the same distance each day in a week.

There are approximately 27.34 yards in 25 meters.

If Erina meets her goal, how many yards will Erina run each day in the third week of her training? Round the answer to the nearest
hundredth.

Enter the answer in the box _____ yards

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joaobezerra joaobezerra · Answer 1 · 2022-01-26T11:10:35+01:00

Using an exponential function, it is found that Erina will run 490.5 yards each day in the third week of her training.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem:

200 meters each day during the first week of her training, hence [tex]A(0) = 200[/tex].

Erina's training goal is to run 150% of the distance she ran each day in the previous week, hence [tex]1 + r = 1.5[/tex]

Then, the equation is:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 200(1.5)^t[/tex]

In the third week, the daily distance in meters that she runs is:

[tex]A(2) = 200(1.5)^2 = 450[/tex]

Since there approximately 27.34 yards in 25 meters, we apply the proportion:

[tex]d = \frac{450}{25} \times 27.34 = 490.5[/tex]

Erina will run 490.5 yards each day in the third week of her training.

You can learn more about exponential functions at https://brainly.com/question/25537936