Question

A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write an exponential growth function to find the sculpture's value in 2006.

a) P(t) = 1200(1 + 0.08)ᵗ; P(6) = $1850.82
b) P(t) = 1200(1 - 0.08)ᵗ; P(6) = $1850.82
c) P(t) = 1200(1 + 0.08)ᵗ; P(6) = $1834.56
d) P(t) = 1200(1 - 0.08)ᵗ; P(6) = $1834.56

Answer 1

The correct exponential growth function to find the sculpture's value in 2006 is P(t) = 1200(1 + 0.08)^t; P(6) = $1850.82.

Step-by-step explanation:

The correct exponential growth function to find the sculpture's value in 2006 is option (a) P(t) = 1200(1 + 0.08)t; P(6) = $1850.82.

In this equation, P(t) represents the value of the sculpture at time t, and the value increases at a rate of 8% per year. The initial value in 2000 is $1200. By plugging in t = 6, we can find that the value in 2006 is $1850.82.