Asma A.

asked • 03/11/14

Doubling time

A population doubles in size every 15 years. Assuming exponential growth, find the annual growth rate. 

Kay G.

Apologies to Asma.  Apparently we have a little disagreement on this point.  In reality, none of us knows what textbook you have, so it's hard telling whether Parviz's comment about "good approximation" is true of your textbook, or if it agrees with Steve.
 
Unfortunately in a situation like this, you sometimes just have to find what seems to fit what your book/class is doing.  That said, since I just now noticed that it's "pre-calculus" it is a question I should have stayed out of, and I apologize to you for that.
Report

03/13/14

3 Answers By Expert Tutors

By:

Steve S. answered • 03/12/14

Tutor
5 (3)

Tutoring in Precalculus, Trig, and Differential Calculus

Parviz F.

Steve:
          Consider:   ek = Pn
                           then :
                           k = n lnp
 
        let p= 1.047
 
                ( 1. 047 ) ^ 15 = 1.991591322
 
           e ^ ( 15 * ln p) = 1.991591322
  
       The answer will come exactly the same. Only one textbook mentions this point. Others just use Slide rule approximation, and don't include the factor of lnp into the calculation, and that is why the anseres are come up different.
Report

03/12/14

Steve S.

If we did use the Compound Interest Formula to find the annual growth rate we would proceed as follows:

A = P(1 + r)^t

2 = 1(1 + r)^15

2^(1/15) = 1 + r

r = 2^(1/15) - 1 ≈ 4.729412282063 %

Notice that this growth rate is larger than the one calculated for the Continuous Exponential growth rate above. AND A(t) is a step function that holds its value for a year after every interest calculation and deposit into the account.
Report

03/12/14

Parviz F. answered • 03/12/14

Tutor
4.8 (4)

Mathematics professor at Community Colleges

Steve S.

You used the wrong mathematical model!
Report

03/12/14

Parviz F.

All text recommend to use either method a good approximation.
 
    Pn = ex
   
    n ln p = X
 
    ( e) ^ 15( ln1.047) = 1.991591322
 
      ( 1.047 ) ^15 = 1.991591322
   
   You see here that if you use lnp in the exponents of e both answers match, but text use Slide rule calculation, and don't include  that  factor into consideration.
  Only one text book brings this point into consideration.
 
 
Report

03/12/14

Kay G. answered • 03/12/14

Tutor
4.9 (34)

~20 Years Accounting Tutoring Experience

Steve S.

You used the wrong mathematical model!
Report

03/12/14

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.