The value k of the exponential growth rate is k = 0.1012
For given situation, we use the formula for exponential growth :
V(t) = V0(1 + k)^t
where, V(t) is the value of the collectors items
V0 is the initial value of painting
k is the exponential growth rate
t is the time interval
A painting sold for $216 in 1977 and was sold again in 1985 for $467.
So, V0 = $216
t = 1985 - 1977
t = 8
V(8) = $467
We need to find k
V(8) = V0(1 + k)^8
467 = 216 * (1 + k)^8
2.162 = (1 + k)^8
taking 8th root on both the sides,
1 + k = ± (2.162)^(1/8)
1 + k = (2.162)^(1/8) or 1 + k = -(2.162)^(1/8)
k = 0.1012 or k = -2.1012
Therefore, the value k of the exponential growth rate is k = 0.1012
Learn more about the exponential growth here:
brainly.com/question/11743945
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