find growth rate

Question

The population of a city is growing according to the exponential model P = Cekt, where P is the population in thousands and t is measured in years. If the population doubles every 11 years what is k, the city's growth rate? [Round answer to the nearest hundredth

Answer 1

Set these parameters:

t = 11
P = 2C


Plug in these values into the model to solve for k.

2C = Ce^11k

 

 

Divide both sides of equation by C.

 

2 = e^11k

 

 

Natural log both sides of the equation.  Bring the exponent of e as that coefficient of the ln.

 

ln(2) = 11kln(e)

 

ln(2) = 11k

 

 

Divide both sides of the equation by 11.

 

ln(2) / 11 = k