Question

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function and find the value of the painting in 25 years.

a) P(t) = 1400(1 + 0.09)ᵗ; P(25) = $5314.27
b) P(t) = 1400(1 - 0.09)ᵗ; P(25) = $5314.27
c) P(t) = 1400(1 + 0.09)ᵗ; P(25) = $2492.50
d) P(t) = 1400(1 - 0.09)ᵗ; P(25) = $2492.50

Answer 1

The correct exponential growth function for the increase in the painting's value is P(t) = 1400(1 + 0.09)t. After 25 years, the value of the painting will be approximately $5314.27, making option a) the correct answer.

Step-by-step explanation:

To find the future value of the painting, we can use an exponential growth function. The general form for exponential growth is P(t) = P0(1 + r)t, where P0 is the original value, r is the growth rate, and t is the time in years. For this example, the original value P0 is $1400, the growth rate r is 9% or 0.09, and we want to find the value after t = 25 years.

So the function becomes P(t) = 1400(1 + 0.09)t. Plugging in 25 for t, we calculate the future value of the painting:

P(25) = 1400(1 + 0.09)25

Using a calculator, we find that P(25) is approximately $5314.27. Therefore, the correct choice is a) P(t) = 1400(1 + 0.09)t; P(25) = $5314.27.