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

Answer:

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

Step-by-step 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

Answer:

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

Step-by-step 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.