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.

b. 2 and 4

step-by-step explanation:

d. all of the above

step-by-step explanation: