Afruit company recently released a new applesauce. by the end of its first year, profits on this product amounted to $24,700.  the anticipated profit for the end of the fourth year is $67,900.  after the first year, the ratio of change in time to change in profit is constant. let x be years and p be profit in dollars.
p(x)=
2. find an equation of the line. write the equation using function notation.
through (6,−5); perpendicular to 4y=x-8
3. find an equation of the line. write the equation using function notation.
through (-3,-8) ; parallel to 2x+3y=5
4. find the equation of the line
through (-11,-4) perpendicular to y=15

1) P(x) =14400x+10300 2)y=-4x+19 3)4) x=-11

(Please check the pictures for better understanding)

Step-by-step explanation:

1) Firstly, let's organize the data. Let the dependent variable x be the years, and the Range P(x) the Profit. So arranging these linear functions y=ax+b and plugging the coordinates for each point (1, 24700) and (4, 67900). Goes:

24,700=x+b

67,900=4x +b

1.1)Solving for b, this Linear System of Equation by the Addition Method goes:

1.2) Now, let's find the slope based on those two points (1, 24700) and (4, 67900) and using the formula to find the slope:

So now we can write this Linear Equation for the Profit:

P(x) =14400x+10300

2) An equation of the line perpendicular to 4y=x-8 has a slope equal to =- the line. In this case, an equation perpendicular to 4y=x-8 .

Rearranging the given equation of the line 4y=x-8 goes:

2.1) The slope of this new line is equivalent to m=-4 since -4 is opposite inverse value for the slope of its perpendicular line (1/4).

If the line passes through the point (6,-5), then this point already belongs to this line.

Then, we can write.

-5=-4(6)+b

-5=-24+b

-5+24=-24+24+b

b=19

Now we can write the function:

y=-4x+19

3) Firstly, let's rearrange the equation. Into a General Equation of the Line y=ax+b

2x+3y=5

-2x+2x+3y=5-2x

3y=5-2x

3.2) Let's find out b, the linear coefficient by plugging the coordinates of the point (-3,-8).

Also, Parallel lines have the same value for the slope such as

-8=-3(-2/3)+b

-8=2+b

-8-2=2-2+b

b=-10

Then the equation of this parallel line is:

4) Now on this last question, we have to find an equation of the line through the point (-11,-4)  perpendicular to another line y=15

Suppose the slope of the first line is and the value of the slope of its perpendicular is

y=15 is a horizontal line with slope equals zero, we can rewrite it as y=0x+15.

Then the slope is zero for horizontal lines.

A perpendicular line to a horizontal line is a vertical one.

In addition to this, a vertical line passes through only one point in the x-axis. Then, there is no horizontal variation. This leads the formula of a slope to an undefinition for Real Set.

The only perpendicular line which passes through the point (-11,-4) to y=15 is the line x=-11.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%

yes

step-by-step explanation:

yes