Question

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

Answer 1

SOLUTION

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

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