Respuesta :
Answer:
a) [tex] P(t) =1600 +50t[/tex]
b) [tex] P(t) = 1600 (1.05)^t[/tex]
Step-by-step explanation:
Assuming the complete question : "A town has a population of 1000 people at time t = 0. In each of the following cases, write a formula for the population, P, of the town as a function of year t. (a) The population increases by 50 people a year. (b) The population increases by 5% a year."
Part a
For this case we can use a linear model in order to estimate the population size since we have a fixed increase each year. So our model would be given by:
[tex] P(t) = P_o + b t[/tex]
Where [tex] b =50[/tex] on this case since represent the increase per year of the slope for the linear model. And the initial amount is [tex] P_o = 1600[/tex], so then the model is:
[tex] P(t) =1600 +50t[/tex]
Part b
For this case we have a rate of increase and when we have this the lineal model is not the most appropiate. So then we can use an exponential model given by:
[tex] P(t) =P_o b^{t}[/tex]
Where [tex] P_o = 1600[/tex] represent the initial population and for this case b is the rate of increase [tex] b = 1+0.05 = 1.05[/tex] since each year we have an increase of 5% and t is the time. So then the model is given by:
[tex] P(t) = 1600 (1.05)^t[/tex]
