Question

A park ranger has determined that the number of trees in his forest is increasing by 3% per year. In 2010, there were 12,000 trees in the forest. Write the equation that represents the number of trees n, in terms of t, the number of years since 2010.

A. n = 12,000(1 + 0.03t)
B. n = 12,000(0.03t)
C. n = 12,000(1.03)^t
D. n = 12,000 - 0.03t

Answer 1

The correct equation that represents the number of trees in terms of the number of years since 2010, with a 3% annual increase, is C. n = 12,000(1.03)^t, which reflects exponential growth.

Step-by-step explanation:

The question involves finding the equation that represents the number of trees n, in a forest in terms of t, the number of years since 2010, given that the number of trees is increasing by 3% per year. To model this situation, we use the exponential growth formula, which in this case is n = 12,000(1.03)^t. This equation assumes that the starting number of trees is 12,000 and that they increase by 3% each year, compounded annually.

Options A, B, and D do not properly account for the compounding nature of percentage growth over time. The correct choice is thus C. n = 12,000(1.03)^t, which is an example of exponential growth where the base 1.03 indicates a 3% increase each year and t is the exponent representing the number of years.