Atown has a population of 1600 people at time =0. in each of the following cases, write a formula for the population p, of the town as a function of year

a)

b)

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:

Where on this case since represent the increase per year of the slope for the linear model. And the initial amount is , so then the model is:

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:

Where represent the initial population and for this case b is the rate of increase since each year we have an increase of 5% and t is the time. So then the model is given by: