Determine what type of model best fits the given situation: the value of a vehicle decreased by 20% each year.

Let value intially be = P

Then it is decreased by 20 %.

So 20% of P =

So after 1 year value is decreased by 0.2P

so value after 1 year will be = P - 0.2P (as its decreased so we will subtract 0.2P from original value P) = 0.8P-------------------------------------(1)

Similarly for 2nd year, this value 0.8P will again be decreased by 20 %

so 20% of 0.8P =

So after 2 years value is decreased by (0.2)(0.8P)

so value after 2 years will be = 0.8P - 0.2(0.8P)

taking 0.8P common out we get 0.8P(1-0.2)

= 0.8P(0.8)

-------------------------(2)

Similarly after 3 years, this value will again be decreased by 20 %

so 20% of

So after 3 years value is decreased by

so value after 3 years will be =

taking common out we get

-----------------------(3)

so from (1), (2), (3) we can see the following pattern

value after 1 year is P(0.8) or

value after 2 years is

value after 3 years is

so value after x years will be ( whatever is the year, that is raised to power on 0.8)

So function is best described by exponential model

where y is the value after x years

so thats the final answer

It is pi over 6:

We first solve this by determining how many times it goes around the circle. When you turn 25pi/6 into a mixed number you get 4pi + 1pi/6. Since it takes 2pi to get around the circle once, you go around the circle twice with 4pi. This leaves with 1pi/6 left at the starting point. The answer is pi/6. 13pi/6 also has the same terminal angle but it is not in range of answers (they are asking for 0-2pi)