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.†
R(t) = 9.04(1.05)t
H(t) = 10.1(0.98)t
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
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: I think something is WRONG with one of our two solutions !!!
P.S. Note that Hungary population is DECREASING by 2% per year!
“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.