Discrete-Time Dynamical Systems

[ponyo]

Hi guys my question is:

Suppose the fraction of individuals with some superior gene increases by 10% each generation.

a)write the discrete-time dynamical system for the fraction of organisms with the gene (denote the fraction at time t and by f_t and figure out the formula for f_t+1

Okay, so for this part I figured that since the fraction of organisms with the superior gene increase by 10% each generation, then my equation would be f_t+1=0.10f_t (10% times the generation at a certain time)

however, my answer is wrong because the full answer in the solutions is f_t+1=0.10f_t+1f_t why did they add 1ft ????

please help explain how to come up with the equation your help is appreciated.

 

[Ishuda]

Hi guys my question is:

Suppose the fraction of individuals with some superior gene increases by 10% each generation.

a)write the discrete-time dynamical system for the fraction of organisms with the gene (denote the fraction at time t and by f_t and figure out the formula for f_t+1

Okay, so for this part I figured that since the fraction of organisms with the superior gene increase by 10% each generation, then my equation would be f_t+1=0.10f_t (10% times the generation at a certain time)

however, my answer is wrong because the full answer in the solutions is f_t+1=0.10f_t+1f_t why did they add 1ft ????

please help explain how to come up with the equation your help is appreciated.

The increase is 10% so you add that to the original amount.