Q9) There are 4,000 students attending a local community college and the number of students is increasing by 5% each year. How many students will attend the college in 4 years? ​

4,862 students will attend the college in the next four years

Step-by-step explanation: If the college starts out with 4,000 students you need to find 5% of 4,000. To do this you would multiply 4,000 by 0.05, you should get 200. So 5% of 4,000 is 200 so the next year there will be 200 more students then last year meaning the next year will have 4,200 student. So now you'll repeat the same step multiply the number of students (now 4,200) by 0.05, then add the answer to the number of students from the previous year. So year two is:

4,200x0.05=210

4,200+210=4,410

repeat these steps till you have four years worth.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

step- i d k and i d c : )

you: : 0

bye