Question

the crime rate of a certain city is increasing by exactly 6% each year. if there were 400 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2019.
round to the nearest whole number.

Explanation:

Step1: Determine the number of years

The time from 1990 to 2019 is \( 2019 - 1990 = 29 \) years.

Step2: Use the compound - growth formula

The formula for compound growth is \( A = P(1 + r)^t \), where \( P \) is the initial amount, \( r \) is the annual growth rate (as a decimal), \( t \) is the number of years, and \( A \) is the final amount.
Here, \( P = 400 \), \( r=\frac{6}{100}=0.06 \), and \( t = 29 \).
Substitute these values into the formula: \( A=400\times(1 + 0.06)^{29} \)
First, calculate \( 1+0.06 = 1.06 \). Then, calculate \( 1.06^{29} \). Using a calculator, \( 1.06^{29}\approx5.4183 \)
Then, \( A = 400\times5.4183=2167.32 \)

Step3: Round to the nearest whole number

Rounding \( 2167.32 \) to the nearest whole number gives \( 2167 \)

Answer:

\( 2167 \)