The crime rate of a city is increasing by 6% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the number of crimes in the year 2018.

Answer 1

This is an exponential growth problem. Crime is up 6% each year from a starting point of 600 in 1990.

If C represents the no. of crimes n years after 1990 and S is the initial value, then the formula is C_n = S(1 + r)ⁿ where r is the percent increase expressed as a decimal. This is the same basic construction for the formula used for compound interest at a bank. n in this problem is 2018 - 1990 = 28 yrs.

C_n = 600(1.06)²⁸ Don't forget that the order of operations says to do the exponent before the multiplication.

1.06²⁸ ≅ 5.112, so Cn = 600 * 5.112 ≅ 3,067 crimes in 2018 at the constant growth rate of 6%/yr.

Answer 2

The equation for this rate of growth would be:

c(t) = 600 * (1 + 0.06)^t

Where t represents years since 1990. To find the answer, we want to evaluate c(2018-1990) or c(28):

c(28) = 600 * (1 + 0.06)²⁸ ≈ 3067.01201829

So there were 3067 crimes in 2018, according to this equation.