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:

both equations and proportions are better.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.