word problem help

Question

Assume the exponential growth model A(t)=A0e^kt and a world population of 6.7 billion in 2003.If the  population must stay below 19 billion during the next 100 years, what is the maximum acceptable annual rate of growth, round down to nearst two decimal places.

Answer 1

Assume:

 

(19 x 10⁹) = (6.7 x 10⁹) (e^100k)

 

and solve for k

 

(19 x 10⁹) / (6.7 x 10⁹)  =  e^100k

 

 

2.835820896 = e^100k

 

ln 2.835820896 = ln e^100k

 

ln 2.835820896 = 100k

 

k = (ln 2.835820896) / 100 

 

ANS : 0.010423315 x 10⁹ = 1.04 x 10⁷ people