The value of a company in millions of dollars during its first 10 years increased by 2% each year. The original valuation of the company was 2.1 million dollars. Write a function to represent the value of the company x years after being founded. How much more was the company worth, in millions of dollars, after 6 years than after 2 years?

Step-by-step explanation:

The rate at which the value of the company increased is exponential.

We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the value of the company after t years.

t represents the number of years.

P represents the initial value of the company.

r represents rate of growth.

From the information given,

P = 2.1 million

r = 2% = 2/100 = 0.02

t = x years

The function to represent the value of the company, x years after being founded is

A = 2.1 × 106(1 + 0.02)^x

Therefore, the worth of the company in 6 years is

A = 2.1 × 106(1 + 0.02)^16

A = 2.1 × 10^6(1.02)^6

2364941

The worth of the company in 2 years is

A = 2.1 × 10^6(1 + 0.02)^2

A = 2.1 × 10^6(1.02)^2

A = 2184840

The difference in worth of the company after 6 years and after 2 years is

2364941 - 2184840 = $180101

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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step-by-step explanation: