Question

The crime rate of a certain city is increasing by exactly 6% each year. If there were 550
crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2016.

Round to the nearest whole number.

Answer 1

Using an exponential function, it is found that the approximate number of crimes in the year of 2016 was of 2502.

What is an exponential function?

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^t$

In which:

• A(0) is the initial value.

• r is the growth rate, as a decimal.

In this problem, there were 550 crimes in the initial year observed, and the growth rate is of 6%, hence the parameters are A(0) = 550, r = 0.06, and the equation is given by:

$A(t) = A(0)(1 + r)^t$

$A(t) = 550(1 + 0.06)^t$

$A(t) = 550(1.06)^t$

2016 is 26 years after 1990, hence:

$A(26) = 550(1.06)^{26} \approx 2502$

The approximate number of crimes in the year of 2016 was of 2502.

More can be learned about exponential functions at https://brainly.com/question/25537936