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Doubling time with exponential growth rate?
Population growth rate = 7.5%
Asking me to calculate exact time needed to double to three decimal points.
Not allowed to use the rule of 70... Prof. posted the solution and I still have no idea how to do it. lol.
Help would be much appreciated. This ln() stuff is relatively confusing. Got a test in the morning :|
4 Answers
- BattleaxeLv 77 years agoFavorite Answer
A = Pe^(r)(t)
2 = e^0.075t
ln2 = 0.075t
0.6931 = 0.075t
t = 9.242 years
- .--
- ptolemy862000Lv 47 years ago
Exponential growth model is determined using this formula
A = Aoe^(kt)
where A is the present population
Ao is the original population
k is the growth rate
t is the time
what is asked in the problem is the time it takes for the
population to double given the growth rate
A = 2Ao substitute this on the equation
2Ao = Aoe^(7.5/100)t
2 = e^(7.5/100)t
taking the natural logarithm of both sides of the equation
In 2 = Ine ^(7.5/100)t
In 2 = (7.5/100)t
t = 100In2 / 7.5
- PhiloLv 77 years ago
Solve 2 = e^(0.075t) ... which assumes continuous growth
take natural log of both sides
ln 2 = 0.075t
0.69315 = 0.075t .... see where the 70 comes from in the rule? ln 2 rounded.
t = 9.24196
- MichaelLv 77 years ago
Well
Po is the initial population
P(t) after t
P(t) = Po (1 + 0.075)^t
so
1.075^t = P(t)/Po = 2
t = ln2 / ln1.075 = 9.584
hope it' ll help !!
