The value of a particular item can be modeled by
p(t) = p0(a)t
where p is in dollars and t is the number of years since the item was purchased. suppose the value of the item increases 5% each year and the item was purchased for $20.

(a) write a formula for p(t) according to the model.
p(t) =

(b) how fast is the value of the item increasing when t = 25 years? round your answer to two decimal places.

$3.29

Step-by-step explanation:

The value of item increases 5% each year and the item was purchased for $20.00.

A. We have to write a formula for P(t) according to the model:

Where, is the initial price, 'r' is the rate of interest. Here in our case it is compounded annually.  

So the formula is:

B. Now we need to find how fast is the value of item increasing when t=25 years.

Differentiating the function we get the rate of change:

(since )

Putting t=25, we get:

So the value of item is increasing by $3.29  each year.

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1