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# Rwanda and Hungary

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you are given models for the population (in millions) of different countries t years after the end of 2005. Determine the year in which the models predict the populations will be equal.†

Rwanda:

R(t) = 9.04(1.05)t

and Hungary:

H(t) = 10.1(0.98)t

Guest Apr 19, 2017
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#1
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Solve for t over the real numbers:
1.05^t = 1.11726 0.98^t

Take the natural logarithm of both sides and use the identities log(a b) = log(a) + log(b) and log(a^b) = b log(a):
0.0487902 t = 0.110876 - 0.0202027 t

Add 0.0202027 t to both sides:
0.0689929 t = 0.110876

Divide both sides by 0.0689929:
Answer: | t = 1.60707 Years

Guest Apr 19, 2017
#2
+82721
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Just set the equations equal  and solve for t

9.04 (1.05)^t   =  10.1(0.98)^t        divide both sides by 9.04

(1.05)^t  =  (10.1 / 9.04) (0.98)^t     divide both sides by (0.98)^t

(1.05)^t / ( 0.98)^t  =  (10.1 / 9.04)     and we can write

(1.05 / 0.98 )^t  =  (10.1 / 9.04)         take the log of both sides

log (1.05 / 0.98)^t  =  log ( 10.1 / 9.04)     and by a log property

t * log ( 1.05 / 0.98)  = log (10.1 / 9.04)    divide both sides by log (1.05/0.98)

t  =   log (10.1 / 9.04) /  log ( 1.05 / 0.98)  ≈  1.607 years ≈  2007

CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
#3
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CPhill: I think something is WRONG with one of our two solutions !!!

P.S. Note that Hungary population is DECREASING by 2% per year!

Guest Apr 19, 2017
#5
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“One of our two solutions”

Now you are clamming credit for the Answer Man’s work.

Plagiarism: The practice of taking someone else's work or ideas and passing them off as one's own.

You practice quite often, but you are not very good at it.  You weren’t very good at embezzlement either.

Guest Apr 19, 2017
#4
+82721
0

Thanks, guest, for the correction.....1.607 yrs is correct.....I punched in a wrong number....!!!

CPhill  Apr 19, 2017

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