Question

The number of bacteria in a colony forms a geometric sequence when counted each hour. The table shows the number of bacteria in the original colony and the number after 2 hours. How many bacteria are there after 1 hour? 5 hours?

Will post table in comments.

Please show all steps! Will give medal!

Answer 1

1.8 = 0.8r^2
r = 1.5
x: 0, 1, 2, 3, 4, 5
y:0.8,1.2, 1.8, 2.7, 4.05, 6.075

Answer 2

What would the formula be before you plugged in 1.8 and 0.8?

Answer 3

@jim_thompson5910

Answer 4

Let r be the common ratio

So to get from term to term, we multiply the term by r.

If the first term is 0.8, then the next term is 0.8*r or just 0.8r

The next term after that is (0.8r)*r = 0.8r^2

But we know that the 3rd term is 1.8, so that means 0.8r^2 = 1.8

Answer 5

Solve for r:

0.8r^2 = 1.8

r^2 = 1.8/0.8

r^2 = 2.25

r = sqrt(2.25)

r = 1.5

Answer 6

So the general term, or the nth term, of the geometric sequence is

\[\LARGE a_n = 0.8(1.5)^{n-1}\]

Answer 7

Oh sorry, n is starting at n = 0, so it should be

\[\LARGE a_n = 0.8(1.5)^{n}\]

Answer 8

If you were to plug in n = 0, you would get 0.8 as a result

and if you were to plug in n = 2, you would get 1.8 as a result

Answer 9

What happens when n = 1?

Answer 10

It's 1.2 when n=1, I think

Answer 11

correct

Answer 12

so 1.2 goes under the '1' in the second row

Answer 13

So for the 3, it would be a3=1.8(1.5)^3 right @jim_thompson5910?

Answer 14

correct, what do you get?

Answer 15

6.075

Answer 16

that is correct

Answer 17

you do the same for n = 4 and n = 5

Answer 18

Okay thanks. :) but for the 6.075, would I just put 6.07 into the table?

Answer 19

I don't see anywhere it tells you to round, so 6.075 is what I would put in that cell

Answer 20

Okay thank you!!

Answer 21

you're welcome