Question

There are multiple parts to this question. I need help with them.

Answer 1

From the table given, the linear model can be drafted from what we were given after using a graphing calculator, see the image below

The linear model can be derived using

`y=ax+b`

Putting in the values we have for a and b into the equation, we have

`y=3.98654x-18.8737`

But from our data, y represents the sales S and x represents time t.

Hence the linear model becomes

`S(t)=3.98654t-18.8737`

Now, let's work on the quadratic model

From the calculator, we have

The quadratic model can be derived using

`y=ax^2+bx+c`

Putting in the values of a, b and c into the equation above, we have

`y=0.104084x^2+1.38443x-4.82228`

So, we know y represents S and x represents t

We have the quadratic model as

`S(t)=0.104084t^2+1.38443t-4.82228`

The exponential model

From the graphing calculator, we have

So, from the image above, the exponential model can be derived using

`y=a(b^x)`

From the image above, substituting the values into the equation, we have

`y=5.61741(1.13292^x)`

Hence the exponential model becomes

`S(t)=5.61741(1.13292^t)`