# A population doubles every 34 years. Assuming exponential growth find the following?

(a) The annual growth rate is __________% per year

(b) The continuous growth rate is ________% per year

Relevance
• A(t) = Ao X 2^(t/34) ..... assume the initial amount is 1 then A(34) = 2

2 = 1 X 2^34/34 = 2 ... see, it works

A(1) = 1 X 2^(1/34) = 1.02059591 = an increase of 0.02059591 in one year .. or 2.059591% per year

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A(t) = (Ao)e^rt

2 = (1)e^(r*34)

34r = ln2

r = 0.020386681

or as a percent .. r = 2.0386681 % continuous

• logic says this is a valid equation.

A(t) = A_o *(2)^(t/34)

(a) annual rate (I think)

need form

A(t) = A_o*( 1+ a.aa)^t

A(t) =A_o* ((2)^(1/34))^t

A(t) = A_o*(1.02059591)^t

A(t) = A_o(1 + 0.02059591)^t

Annual Rate = 2.0589591 %

so for continuous rate (I'm sure is ) :

so to get (b) convert to

form A(t) =A_o*e^(kt)

A(t) = A_o*e^(ln(2)t/34)

so k = ln(2)/34 = 0.020386682

Continuous Rate = 2.038666 %

• a) %growth = 70/DoublingTime = 2%

b)same as a i think