in 2004, an art collector paid $69,099,000 for a particular painting. the same painting sold for $29,000 in…

in 2004, an art collector paid $69,099,000 for a particular painting. the same painting sold for $29,000 in 1950. complete parts (a) through (d). a) find the exponential growth rate k, to three decimal places, and determine the exponential growth function v, for which v(t) is the painting’s value, in dollars, t years after 1950. v(t)=29000e^0.144t (type an expression. type integers or decimals for any numbers in the expression. round to three decimal places as needed.) b) predict the value of the painting in 2026. $ (round to the nearest million as needed.)

in 2004, an art collector paid $69,099,000 for a particular painting. the same painting sold for $29,000 in 1950. complete parts (a) through (d). a) find the exponential growth rate k, to three decimal places, and determine the exponential growth function v, for which v(t) is the painting’s value, in dollars, t years after 1950. v(t)=29000e^0.144t (type an expression. type integers or decimals for any numbers in the expression. round to three decimal places as needed.) b) predict the value of the painting in 2026. $ (round to the nearest million as needed.)

Answer

Explanation:

Step1: Determine the value of t for 2026

The base - year is 1950. For 2026, $t = 2026 - 1950=76$.

Step2: Use the exponential - growth function

The exponential - growth function is $V(t)=29000e^{0.144t}$. Substitute $t = 76$ into the function: $V(76)=29000e^{0.144\times76}$. First, calculate $0.144\times76 = 10.944$. Then, $e^{10.944}\approx52999.777$. Finally, $V(76)=29000\times52999.777 = 1536993533$. Rounding to the nearest million, $V(76)\approx1537000000$.

Answer:

$1537000000$