Net Worth Growth Calculation of a Company
How is the net worth of the company expected to change between 2020 and 2030?
How much is the net worth of the company expected to change during the mentioned time frame?
If the company is worth $40,000 in 2020, what is it worth in 2030?
What is the anticipated net worth of the company in 2030 based on its value in 2020?
Answer:
The change in net worth of the company between 2020 and 2030 will be $20,000.
The net worth of the company in 2030 is $20,000.
The data provided indicates that the company's net worth, denoted as f(t), is increasing at a rate of f'(t) = 2000 - 12t^2 dollars per year, with t representing the number of years since 2020.
To determine how the company's net worth is expected to change between 2020 and 2030, the integral of f'(t) with respect to t over this period needs to be found.
By integrating each term separately, we get F(t) = 2000t - 4t^3 + C, where C is the constant of integration. Utilizing the information that the company is worth $40,000 in 2020, the constant of integration is calculated to be 40000, resulting in the function F(t) = 2000t - 4t^3 + 40000.
The change in the net worth of the company between 2020 and 2030 is determined by evaluating F(10) - F(0), resulting in a change of $20,000. Additionally, the net worth of the company in 2030, calculated as F(10), is found to be $20,000.