Question

The Library of Congress in Washington, D.C. is the largest library in the world. It contains nearly 126 million items. The library adds about 10,000 items to its collection daily. Write a rule that describes the number of items in the Library of Congress as a function of the number of items added daily. Then find the number of days it will take the library to reach 150 million items.

Answer 1

Using the function I(d) = 126,000,000 + 10,000d, where I is the number of items and d is the number of days, it will take 2,400 days for the Library of Congress to add enough items to reach a total of 150 million items.

Step-by-step explanation:

To determine the number of days it will take for the Library of Congress to reach 150 million items, we should first establish the rule to describe the library's collection as a function of the number of items added daily. The Library of Congress starts with a known quantity of 126 million items and adds approximately 10,000 items each day.

The function describing this can be written as:

I(d) = 126,000,000 + 10,000d

where I represents the total number of items and d represents the number of days.

To find the number of days needed to reach 150 million items, we can set the function equal to 150,000,000:

150,000,000 = 126,000,000 + 10,000d

Solving for d gives us:

150,000,000 - 126,000,000 = 10,000d

24,000,000 = 10,000d

d = 24,000,000 / 10,000

d = 2,400

Therefore, it will take 2,400 days for the Library of Congress to reach 150 million items.