Question

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?

Answer 1

Answer:

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