If the annual decrease in the population of a town is 15% and the present population of the town is 32000 , then what will be the population of the town after 3 years ?

Options

A. 21454
B. 18042
C. 19652
D. 19008

Explanation

To find the population of the town after 3 years with an annual decrease of 15%, we can use the formula for exponential decay:

\[ P = P_0 \times (1 - r)^t \]

Where:
- \( P \) is the future population,
- \( P_0 \) is the present population,
- \( r \) is the rate of decrease (as a decimal),
- \( t \) is the number of years.

### Step 1: Identify the values
- Present population \( P_0 = 32000 \)
- Rate of decrease \( r = 15\% = 0.15 \)
- Time \( t = 3 \) years

### Step 2: Substitute the values into the formula
\[ P = 32000 \times (1 - 0.15)^3 \]

### Step 3: Calculate \( (1 - 0.15) \)
\[ 1 - 0.15 = 0.85 \]

### Step 4: Raise \( 0.85 \) to the power of 3
\[ 0.85^3 = 0.85 \times 0.85 \times 0.85 \]
Calculating this:
- \( 0.85 \times 0.85 = 0.7225 \)
- \( 0.7225 \times 0.85 = 0.614125 \)

### Step 5: Multiply by the present population
\[ P = 32000 \times 0.614125 \]

Calculating this:
\[ P = 32000 \times 0.614125 = 19645.6 \]

### Step 6: Round to the nearest whole number
Since population must be a whole number, we round \( 19645.6 \) to \( 19646 \).

### Final Answer:
The population of the town after 3 years will be approximately **19,646**.

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