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

Solution:

The Given model to Predict the population

$P=P_{0}(1.005)^{\frac{t}{3}$

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

The population increases by 0.5 % every n months.

Initial Population = 215

Final Population

$=215+215\times \frac{0.5}{100}\\\\=215+1.075\\\\=216.075$

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

$216.075=215\times (1.005)^{\frac{t}{3}}\\\\ (1.005)^{\frac{t}{3}}=\frac{216.075}{215}\\\\ (1.005)^{\frac{t}{3}}=(1.005)^{1}\\\\ \frac{t}{3}=1\\\\ t=3$

t=3 years =36 months

The value of n is equal to 36 months.