Question

In 2006, 5,200 highway accidents were recorded in a city. The number of highway accidents increases by 5% every year. Let y represent the number of highway accidents x years since 2006. Which type of sequence does the situation represent? A. The situation represents a geometric sequence because the sucessive y- values have a common ratio of 1:5. B. The situation represents a arithmetic sequence because the sucessive y-values have a common difference of 1.05. C. The situation represents a geometric sequence because the sucessice y-values have a common ratio of 1.05. D. The situation represents a arithmetic sequence because the sucessive y-values have a common difference of 1.5

Answer 1

C. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05

Explanation:

We are given

In 2006, 5,200 highway accidents were recorded in a city

The number of highway accidents increases by 5% every year

Let y represent the number of highway accidents x years since 2006

Since, 5% is increasing every year of previous number

so, this is geometric series

In 2006 :

x=0

`y_0=5200`

now, we can use formula

i=5%=0.05

`y=y_0(1+i)^(x)`

now, we can plug values

`y=5200(1+0.05)^(x)`

`y=5200(1.05)^(x)`

now, we can compare with nth terms of geometric series

`a_n=a_1(r)^n`

where r is the common ratio

so, we can find r

`r=1.05`

so, common ratio is 1.05

Answer 2

C. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Explanation:

The initial number of accidents = 5200 = Po

It increases 5% every year.

So r = 5% = 0.05

y = Po(1 + r)^x

y = 5200(1 + 0.05)^x

y = 5200(1.05)^x

This sequence is an exponential. Which is a geometric sequence.

Answer: C. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Thank you.