The population of centerville increases each year. the function c(t) = p(1 +r)^t represents the population of centerville at year t, where p is the initial population and r is the rate of increase. select the correct statement. a. the factor (1 + r) is the percentage by which the population grows each year. b. the value of c depends only on starting population and year. c. r is less than 0. d. p represents the population in year 0

P represents the population in year 0 ⇒ D

Step-by-step explanation:

* Lets explain the exponential growth function

- The exponential growth function is f(x) = a (1 + r)^t, where a is the initial

  amount (at t = 0), (1 + r) is the factor of growth , r is the rate of growth

  in decimal ant is the time of growth

* Lets solve the problem

∵ The function C(t) = P(1 + r)^t represents the population of

  centerville at year t, where P is the initial population and r is the

  rate of increase

- Ex: If your investment is increased 10% annually, then that means

 each year, your total has multiplied itself by 110% (the growth factor

 is 1 + 10/100 = 1.1)

∴ (1 + r) is the factor grows each year

∵ C(t) = P(1 + r)^t

∴ C depends on P(starting population) , r(the increasing rate and

   t(the time in year)

∵ r is the rate of increase means the percentage of increasing , then

  0 < r < 1

∴ r is not less than 0

∵ P is the initial amount when t = 0

∴ P represents the population in year 0