Question

A particular famous painting was purchased for $720,000 in the year 2021. The value has been increasing at the continuous rate of 10% per year. Write an equation for y , the value at time t , that represents the situation where t = 0 represents the year 2021. y = Incorrect dollars Find the value of the famous painting in the year 2028.

Answer 1

The equation for the value of a famous painting growing at a continuous rate of 10% per year is y = 720000(1 + 0.10)^t. The value of the painting in the year 2028 is $1,457,272.80.

Step-by-step explanation:

To write the equation for the value of the famous painting at time t, we can use the formula for exponential growth: y = A(1 + r)t, where y is the value at time t, A is the initial value, and r is the growth rate as a decimal.

In this case, the initial value is $720,000 and the growth rate is 10% per year, or 0.10. So the equation becomes y = 720000(1 + 0.10)t.

To find the value of the painting in the year 2028, we need to substitute t = 2028 - 2021 = 7 into the equation. This gives us y = 720000(1 + 0.10)7. Evaluating this expression gives us a value of $1,457,272.80.

Learn more about Exponential growth