Question

The number of fires reported each year in a major United States city has been increasing at a rate of 6 percent per year. The number of fire reported for the year 1986 was 15,000. If the number of fires continues to increase at the same rate, how many will be expected in 1996.

Answer 1

26,863 fires

Explanation:

Since the number of fires is increasing at a rate of 6%, this problem can be modeled using an exponential growth model.

`N(t)=N_0(1+r)^t`

• The number of fires in 1986, No = 15,000

,

• The rate of increase, r = 6% = 0.06

,

• Time, t = 1996 - 1986 = 10 years

We want to find the value of N(t) when t=10.

Substitute the given values into the formula:

`\begin{gathered} N(10)=15,000(1+0.06)^(10) \\ =15,000(1.06)^(10) \\ =26862.7 \\ \approx26,863 \end{gathered}`

If the number of fires continues to increase at the same rate, the number of fires in 1996 will be approximately 26,863.