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dmitriy555 [2]
1 year ago
6

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

Mathematics
1 answer:
Natalija [7]1 year ago
8 0

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)

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To solve this we are going to use the future value of annuity due formula: FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]
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k is the number of deposits per year

We know for our problem that P=420 and t=15. To convert the interest rate to decimal form, we are going to divide the rate by 100%: r= \frac{10}{100} =0.1. Since Ruben makes the deposits every 6 months, k=2. The interest is compounded semiannually, so 2 times per year; therefore, k=2.
Lets replace the values in our formula:

FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]
FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]
FV=29299.53

We can conclude that the correct answer is <span>$29,299.53</span>
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