A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

I am so confused on how to find the exponential model. Please help! Find the exponential growth or decay model y = aebt or y = ae−bt for the population of each country by letting t = 10 correspond to 2010. They give two points and want us to find the exponential model. (2010, 8.6) and (2020, 7.4)

  • This Question is Closed
  1. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so the 2 points are for the one model... (2010, 8.6) and (2020, 7.4) is that correct..?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  3. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok... so there a 2 numbers you need to find, a = the initial population b = the growth constant... so using the 2 points you get 2010 \[8.6 = ae^{10b}\] 2020 \[7.4 ae^{20b}\] does that make sense...?

  4. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2020 should read \[7.4 = ae^{20b}\]

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes I understand that. Are you supposed to solve for a next?

  6. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes... so looking at the 2020 information you can use index laws for the same base to rewrite it as \[7.4 = e^{10b} \times ae^{10b}\] does that make sense..?

  7. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then making a substitution for the 2010 information \[7.4 = 8.6 \times e^{10b}\] now you can solve for b

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so b=0.0860465116?

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, forgot a step. b=-.0150282203. Is that correct?

  10. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    not quite its \[\frac{7.4}{8.6} = e^{10b}\] now take the ln of both sides so you can solve for b \[\ln(\frac{7.4}{8.6}) = 10b\] now solve... b needs to be a negative... because the population has declined

  11. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    great... so you have a decay model... next you need to substitute the value of b into either equation to find the initial population, a

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That is where I get confused....

  13. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[8.6 = a \times e^{-0.0150282203 \times 10}\]

  14. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so \[\frac{8.6}{e^{-0.0150282203 \times 10}} = a\]

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    9.99459=a Is that correct?

  16. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's what I got... so now you have your model... you can check a and b using the 2nd equation when t = 20 to see if you get 7.4

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh my goodness thank you soooo much! For some reason I just could not think to divide.....that last part has had me stumped! Now I can breathe a sigh of relief. You are the best!

  18. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good luck

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.