Question

The number of books in a small library increases according to the function B(t) = 6300 e 0.05t, where t is measured in years.

1. How many books will the library have after 5 years? B(5) =

A) 6939.13
B) 6859.20
C) 7024.61
D) 7112.42
2. When will the library have 14,000 books in their collection? Time for B(t) = 14,000. t =

A) 13.34 years
B) 12.98 years
C) 14.22 years
D) 15.05 years

Answer 1

After 5 years, the library will have approximately 8,141.78 books, not matching the provided options, suggesting an error in the student's information. The library will have 14,000 books after about 14.22 years.

Step-by-step explanation:

The number of books in a small library increases according to an exponential function B(t) = 6300 Ⅰ, where t is measured in years. To solve the given problems, we'll apply the exponential growth formula given in the question:

1. How many books will the library have after 5 years? For B(5), substitute 5 for t in the function B(t) = 6300e0.05×5 to calculate the number of books, leading to a calculated value of approximately 8,141.78 books, which was not one of the provided options. There may be a mistake in the options provided by the student or in the question itself.
2. To find when the library will have 14,000 books, we set B(t) = 14,000 and solve for t using the natural logarithm. This calculation leads to t being approximately 14.22 years, which is option C.