Question

How do I tell if a data set is represented by an exponential function if I have no given f(0)? My reasoning being that if I did, I could use y = Pe^(rt)

Answer 1

you mean for example you are given something like

x y
1 1
2 4
3 9
4 16

like that?

Answer 2

yeah

Answer 3

well you could still use y = Pe^(rt) in a way

Answer 4

is this related to exponential growth?

Answer 5

yes

Answer 6

let's say for example you are given that at t = 2 seconds, a DNA consists of 40 strands. Then, at 4 seconds, the DNA consists of 100 strands. How many DNA strands will there be at 10 seconds?

so you have t = 2 and t = 4. You set up the equation like this

y = Pe^(rt)

\[100 = 40e^{r(4-2)}\]
\[100 = 40 e^{2r}\]
so now..you can solve for r

Answer 7

does that help?

Answer 8

@jcd2012 still there?

Answer 9

ya let me look at what you said

Answer 10

tell me when you get it

Answer 11

so I did what you did for my problem and got r. what next?

Answer 12

in my problem... i asked how many DNA strands there will be in 10 seconds. so i have t = 2 seconds and t = 10 seconds

\[y = Pe^{rt}\]
\[y = 40e^{r(10 - 2)}\]
now you just substitute the value of r there and you can solve for y

Answer 13

I did that for a known y-value on the data set and the result was not the same

Answer 14

how can you know the y-value of the data if it's not given?

Answer 15

that's what I'm saying. I'm trying to algebraically show that the data set is from an exponential function when I don't know (0,y)

Answer 16

hmm you want to solve for the value of y at t = 0...let's use the same problem

at t = 2, DNA strand is 40 so let's solve how many strands at t = 0

\[y = Pe^{rt}\]
\[40 = Pe^{r(2 - 0)}\]
substitute r there then you can solve for P

Answer 17

by the way... if you notice, the formula i'm using here is:
\[\huge y = Pe^{r(t_2 - t_1)}\]
where:
y is the final value
P is the initial value
r is the constant
t2 is the final time
t1 is the initial time

Answer 18

still don't have it...

Answer 19

tell me what the value of r is...

Answer 20

What am I going to get from that? Does it work in your equation? It doesn't in mine

Answer 21

hmm.. let me solve my problem to show you how to do it...

Answer 22

let's say for example you are given that at t = 2 seconds, a DNA consists of 40 strands. Then, at 4 seconds, the DNA consists of 100 strands. How many DNA strands were there initially?
\[y = Pe^{rt}\]
\[\implies 100 = 40e^{r(4-2)}\]
\[\implies 100 = 40 e^{2r}\]
\[\implies \frac{100}{40} = e^{2r}\]
\[\implies 2.5 = e^{2r}\]
\[\implies \ln(2.5) = 2r\]
\[\implies 0.9163 = 2r\]
\[\implies 0.4582 = r\]

now... to solve for P at t = 0
\[y = Pe^{rt}\]
\[\implies 40 = Pe^{0.4582(2 - 0)}\]
\[\implies 40 = Pe^{0.9163}\]
\[\implies 40 = P(2.5)\]
\[\implies 16 = P\]
so there were 16 strands at t = 0

Answer 23

do you get it now?

Answer 24

yeah. thanks for sticking it out with me

Answer 25

welcome