How to type a line above the number 6 on chromebook.
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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
We want to find 
, for
.
Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:
.
Thus,
![y'=[(x^2+2)^3]'[(x^3+3)^2]+[(x^3+3)^2]'[(x^2+2)^3]\\\\ =3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3](https://tex.z-dn.net/?f=y%27%3D%5B%28x%5E2%2B2%29%5E3%5D%27%5B%28x%5E3%2B3%29%5E2%5D%2B%5B%28x%5E3%2B3%29%5E2%5D%27%5B%28x%5E2%2B2%29%5E3%5D%5C%5C%5C%5C%20%3D3%28x%5E2%2B2%29%5E2%28x%5E3%2B3%29%5E2%2B2%28x%5E3%2B3%29%28x%5E2%2B2%29%5E3)
Answer: A)
.
Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:
Thus,
Answer: A)