Final answer:
To calculate the value of a painting in 2023 if its value doubles each year from its initial value in 2020, you can use the mathematical formula for exponential growth: F = P * (2^n). In this case, the equation simplifies to k * (2^3), or k * 8 where 'k' is the initial value.
Step-by-step explanation:
The subject of this question is exponential growth, a principle in mathematics. If the value of a painting is k dollars in 2020 and it's supposed to double each year, then to find the value in 2023 we need to consider how many years are between 2020 and 2023. There are 3 years, which means the painting's value will double 3 times.
To represent this process mathematically, we could use the formula for exponential growth: F = P * (2^n), where F is the future value, P is the present value (or the initial amount), and 'n' is the number of times that the amount doubles.
In this case, 'F' is the value of the painting in 2023, 'P' is the initial value (k dollars in 2020), and 'n' is 3 (since 3 years have passed from 2020 to 2023). Substituting those values into the formula, the expression for the value of the painting in 2023, if it doubles each year, would be k * (2^3), or k * 8.
Learn more about Exponential Growth