The number of trees in a town is 17640. If the number of trees increases annually at the rate of `5%,` how many tress were there 2 years ago ?

Options

A. 1400
B. 15000
C. 16000
D. 19450

Answer

To find out how many trees were there 2 years ago in the town, we can use the concept of compound interest since the number of trees increases annually at a rate of 5%.

Let's denote:
- The number of trees now (after 2 years) = 17640
- The annual increase rate = 5% = 0.05
- The number of years = 2

We can use the formula for compound interest to find the initial amount (the number of trees 2 years ago):

\[ A = P(1 + r)^n \]

Where:
- \( A \) = the amount of trees after \( n \) years (17640)
- \( P \) = the initial amount of trees (what we want to find)
- \( r \) = the rate of increase (5% or 0.05)
- \( n \) = the number of years (2)

Rearranging the formula to solve for \( P \):

\[ P = \frac{A}{(1 + r)^n} \]

Substituting the known values into the equation:

\[ P = \frac{17640}{(1 + 0.05)^2} \]

Calculating \( (1 + 0.05)^2 \):

\[ (1 + 0.05)^2 = (1.05)^2 = 1.1025 \]

Now substituting this back into the equation for \( P \):

\[ P = \frac{17640}{1.1025} \]

Calculating \( P \):

\[ P \approx 16000 \]

Thus, the number of trees 2 years ago was approximately **16,000**.