Question

Suppose a tortoise is 2300 feet from the ocean. Each day the tortoise travels one-third of the remaining distance to the ocean.

(i) Which of the following models could be used to predict the distance that the tortoise must travel to reach the ocean?
O A. (2300)=
0B.(号)严
O c. 2300(2)=
O D. [2300(7)]*
(il) Use your model to compute the remaining distance to ocean after 5 days of travel.
(Express your answer rounded correctly to the nearest tenth of a foot.)
Answer =

Answer 1

The correct model is 2300(\(\frac{2}{3}\))^n, and after 5 days, the tortoise would have 302.9 feet remaining to reach the ocean.

Step-by-step explanation:

The correct model to predict the distance that the tortoise must travel to the ocean after traveling each day one-third of the remaining distance is 2300(\(\frac{2}{3}\))^n, where n is the number of days traveled. Each day the tortoise covers one-third of the distance to the ocean, which leaves two-thirds of the distance for the next day.

After 5 days, using the model 2300(\(\frac{2}{3}\))^5, the computation is as follows:

1. 2300 * (\(\frac{2}{3}\))^1 = 1533.3 (after 1 day)
2. 1533.3 * (\(\frac{2}{3}\))^1 = 1022.2 (after 2 days)
3. 1022.2 * (\(\frac{2}{3}\))^1 = 681.5 (after 3 days)
4. 681.5 * (\(\frac{2}{3}\))^1 = 454.3 (after 4 days)
5. 454.3 * (\(\frac{2}{3}\))^1 = 302.9 feet (rounded to the nearest tenth, after 5 days)

The remaining distance to the ocean after 5 days of travel is 302.9 feet.