Question

The population of a town after t years is represented by the function f(t)=19,350(0.976)t . What does the value 0.976 represent in this situation?

a.The population of the town increases by 0.976 each year.

b.The initial population of the town is 0.976.

c. The population of the town is 0.976 times the population of the town in the previous year.

d. The population of the town decreases by 0.976 each year.

Answer 1

c. The population of the town is 0.976 times the population of the town in the previous year.

Answer 2

The population of a town after t years is represented by the function f(t)=$19,350(0.976)^t$

If P be the initial population of a town, r be the rate of increase or decrease  after time t, Then Final population:

$P_{f} {\text{is given by} = P (1 \pm r)^t$ if there is a positive sign between 1 and r , it means population is increasing.And if there is negative sign between 1 and r , it means population is decreasing.

As value of (1 $\pm$ r) is less than 1 , it means Population is decreasing.

Option (C) is correct option, which is The population of the town is 0.976 times the population of the town in the previous year.

You must be thinking why option D is not true, because the word "times" has not been used in the statement of option D which is   The population of the town decreases by 0.976 each year.