Question

Find the exponential model y=ae^bx that fits the points (0,2) and (4,3)

How on earth would you even begin to do this?

Answer 1

Try substituting in these points and see what happens.

(0,2) and (4,3)

Answer 2

y = a*e^(bx) for (4,3)

3 = a* e ^ (b*4)

3 = a*e^(4b)

Answer 3

2 = a * e
3 = a*e^(4b)
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Can these be solved simultaneously? @svan14

Answer 4

I'm not sure what you mean, but the back of my book says that the answer should be y=2e^.1014x @Directrix

Answer 5

I mean to solve for a and solve for b and substitute those values into the equation y=a*e^(bx)

Answer 6

I really don't know...I'm totally lost on my assignment, I was sick, since I have no idea what I am doing, I'll just have to go in early tomorrow, get down on my hands and knees and beg my teacher to help me understand what the heck went on in class. So basically what I'm saying is it's okay if we can't figure out this question,(you can move onto other questions) Thanks for your help anyways! I really really really, (lots of reallys here) appreciated it! @Directrix

Answer 7

I want to re-do the first calculation.

y=a*e^(b*x) for (0,2)

2 = a* e^(b*0)

2 = a* e ^ 0

2 = a * 1

2 = a

a = 2 ===> Corrected Value

Answer 8

We know a = 2 now.

y=2* e^ (bx)

Now, if we had the value of b, we could substitute that in and we'd have the exponential curve that passes through the two given pointsl

Answer 9

couldn't we just plug in one of the x and y values plus what we just found for a and solve for b?

Answer 10

From above,

3 = a*e^(4b)

3 = 2* e^(4b) I think we will have to take natural logs of both sides to solve for b.

Answer 11

From above,

3 = a*e^(4b)

3 = 2* e^(4b) I think we will have to take natural logs of both sides to solve for b.

Answer 12

>>couldn't we just plug in one of the x and y values plus what we just found for a and solve for b?

Try that and see what you get.

Answer 13

would you start by dividing both sides by 2?

Answer 14

no wait you would do that thingy with the ln so it gets rid of the e......i don't know anymore....

Answer 15

Follow through on your ideas to see if they work.

Answer 16

Solve for b:

3 = 2* e^(4b)

3/2 = e^(4b)

Answer 17

ln(1.5) = ln ( e^(4b) )

ln(1.5) = 4b * ln e

ln (1.5) = 4b * 1

ln(1.5) / 4 = b

b = ? @svan14 Will you solve for b? Get the natural log of 1.5 and then divide that by 4.

Answer 18

If you solve for b, this problem will end.

Answer 19

YEAH!!!! I finally got the same answer as the back of the book for "a" !!! Then I just plug a back into the equation that we first used and 2 that we got earlier, so it would be y=2e^.10139x! THANK YOU!!!!! (my math teacher scares me!!!!) Sorry this took 40,000 years to solve!

Answer 20

you probably deserve to be president or something....

Answer 21

I ran this through: ln(1.5) / 4 = b

and got b = .1014 to the nearest ten-thousandth.

Answer 22

Okay, we got it done.

Answer 23

(high five! Sorry I have cold hands!)