Question

The crime rate of a certain city is increasing by exactly 2 % 2 % each year. If there were 450 450 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2017 2017 .

Answer 1

768 crimes

Explanation:

we know that

The equation of a exponential growth function is equal to

`y=a(1+r)^x`

where

y ----> is the number of crimes

x ----> is the number of years since 1990

r is the rate of chance

a is the initial value

we have

`a=450\ crimes\\r=2\%=2/100=0.02`

substitute

`y=450(1+0.02)^x`

`y=450(1.02)^x`

Determine the approximate number of crimes in the year 2017

Find the value of x

`x=2017-1990=27\ years`

substitute the value of x

`y=450(1.02)^(27)=768\ crimes`