# Question #e8dd9

##### 3 Answers

See below.

#### Explanation:

Given a model

and a set of points

We will try to adjust the model to the

The determination of

so we have to solve the linear system

where

and

Putting numeric values into the formulas we get

obtaining

Attached a plot showing the results.

Answering the requested items:

a) Using an square minimum error criteria, the parameters are:

b) The stock appreciation is linked to a positive rate so

This is attained for

c) The stock loses value for

Given that

Let us consider

so

From (2) and (3) we get

Hence

**(a)**

**(b)**

Now the given equation becomes

Differentiating this equation w,r to t we get the rate of change of the price of stock as

In this equation the value of

So rate of positive change of price of stock will occur in this period i.e. Jan every year this means the stock appreciate s most in this period.

**(c)**

Taking

when t =4

Again

when t =8

So during the period **May -September** growth of price gets diminished i.e the price of the stock is actually **losing in this period.**

Alternate solution for part (c)

#### Explanation:

For Solution posted by @dk_ch

The modelling equation becomes

#f(t)=2.5t+20+10sin((pit)/6)#

Using inbuilt graphics tool the plotted equation looks like

The maximum and minimum of the curve are located for

As such the stock actually lost value from May to August.

--.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-..-

For Solution posted by @Cesareo R

#f(t)=2.25t+18.49+7.29sin((pit)/6)# , values rounded to two decimal places

Using inbuilt graphics tool the plotted equation looks like

The maximum and minimum of the curve are located for

As such the stock actually lost value from May to August.