Aculture of bacteria doubles every 2 hours.
a. explain how this situation can be modeled with a sequence.
b. if there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

2,048,000.

Step-by-step explanation:

a. Let the initial number of bacteria = x

Since bacteria doubles every 2 hours, so the sequence will be in the form of

x, 2x, 4x, 8x, .........

This sequence is a geometric sequence with a common ratio of 2.

b. Since explicit formula for a geometric sequence is

Where, = population of bacteria after n hours.

            = Initial population

            r = common ratio

            n = number of times population got doubled

By putting the values of each term in the formula :

      =

      = 2,048,000

After 24 hours population of bacteria would be 2,048,000.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

lol.

it's ok we all do this sometimes.

-aparri