Question

so im doing a portfolio project and i have to write a rule for this chart that i just made which is explaining the growth of bacteria my chart is - 1hr=16 2hr=256 3hr=4096 4hr=65386 5hr=1048576 6hr=16777216 its multplies each hr. by 16. but how would i write that rule to be true. cause i dont think xtimes16 is correct

Answer 1

you want an exponential function, really.

Answer 2

Let's look at what exponential functions mean in general.
I won't complicate by considering negative exponents, just a \(«\)real\(»\) example.

Answer 3

Can you give me the rule and ill fill in the numbers. If i have the "rule" i can figure the rest out.

Answer 4

Ok, the exponential function (the "rule" you asked for) is:
\(\color{#000000}{ \displaystyle f(x)=a\cdot (b^x) }\)

Answer 5

a - is the initial population
b - the growth factor (times which you multiply every year/month/day or whatever time-frame you are using)

Answer 6

Now, and example ...

Answer 7

okay ima write it and solve it and if i think i did it right ill put it up here and you can like check it or whatever

Answer 8

never mind i dont see how this works at all with the table. what would i put for the exponent

Answer 9

EXAMPLE: Sam has two cancer cells in his body,
and every day cancer cells triple. How do you
represent this situation as a function of time?
\(\text{----------------------------------------------------------}\)
You know that before the first day has passed
(i.e. when t=0), Sam has 2 cells. So, record:
\(\color{#000000}{ \displaystyle t=0\quad\quad \quad y=2 }\)

Next, after every new day passes, Sam's cancer
cells triple. That means that you can record:
\(\color{#000000}{ \displaystyle t=1\quad\quad \quad y=6 }\)

Note that I said t=1, for day 1, and since 1 day
has passed, I multiply the y-value times 3 (b/c
the cells triple daily).

Abiding this pattern that cancer triple each day,
I get the following:

\(\color{#000000}{ \displaystyle t=0\quad\quad \quad y=2 }\)
\(\color{#000000}{ \displaystyle t=1\quad\quad \quad y=2\times 3=6 }\)
\(\color{#000000}{ \displaystyle t=2\quad\quad \quad y=2\times 3^2=18 }\)
\(\color{#000000}{ \displaystyle t=3\quad\quad \quad y=2\times 3^4=54 }\)

and after \(t\) days, I have:
\(\color{#000000}{ \displaystyle y=2\times 3^t }\)

So, you can record:
\(\color{#000000}{ \displaystyle y=2\times 3^t }\)

Answer 10

it is a fairly difficult topic when first introduced, and if there are difficulties understanding, I get it. I hope tho' that this is a helpful example.