A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

From 1953 to 1966 the number of automobiles in the country increased at an annual rate of 6.7 percent. What is the doubling time for growth in automobiles in the US?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Annual increase is 6.7% . If initially N automobiles were there in 1953 After 1 year the no. of automobiles is (106.7/100)*N. After 2 years i.e, in 1955 it'll be (1.067)*(1.067)*N Similarly after x years it'll be $$(1.067)^{x} \times N$$ Make it equal to 2N since we need to find the time taken to double. $$(1.067)^x=2 \implies x=\frac{\ln2}{\ln1.067}=10.7$$ It takes ~11 yrs for the doubling of the automobiles.

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

    Or: \[1.067^{x}=2 => x =\log_{1.067} 2\approx10.7\]

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

    Thank-you to both of you!

  4. 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.