Question

P = 215 (1.005)t/3 the equation above can be used to model the population, in thousands, of a certain city t years after 2000. according to the model, the population is predicted to increase by 0.5% every n months. what is the value of n

Answer 1

As t/3 it means that 0.5% every 3 years.

So n will be 3 years , 36 months

Answer 2

The Given model to Predict the population

`P=P_(0)(1.005)^{(t)/(3)`

----------------------------------(1)

The population increases by 0.5 % every n months.

Initial Population = 215

Final Population

`=215+215* (0.5)/(100)\\\\=215+1.075\\\\=216.075`

Substituting the value of , Initial and final Population in equation 1,

`216.075=215* (1.005)^{(t)/(3)}\\\\  (1.005)^{(t)/(3)}=(216.075)/(215)\\\\  (1.005)^{(t)/(3)}=(1.005)^(1)\\\\ (t)/(3)=1\\\\ t=3`

t=3 years =36 months

The value of n is equal to 36 months.