A painting sold for $246 in 1980 and was sold again in 1985 for $439. Assume that the growth in the value V of the collector's item was exponential. ... a) Find the value k of the exponential growth rate. Assume V₂ = 246. k= (Round to the nearest thousandth.) b) Find the exponential growth function in terms of t, where t is the number of years since 1980. V(t) = c) Estimate the value of the painting in 2007. $ (Round to the nearest dollar.) d) What is the doubling time for the value of the painting to the nearest tenth of a year? years (Round to the nearest tenth.) e) Find the amount of time after which the value of the painting will be $6430. years (Round to the nearest tenth.)
A painting sold for $246 in 1980 and was sold again in 1985 for $439. Assume that the growth in the value V of the collector's item was exponential. ... a) Find the value k of the exponential growth rate. Assume V₂ = 246. k= (Round to the nearest thousandth.) b) Find the exponential growth function in terms of t, where t is the number of years since 1980. V(t) = c) Estimate the value of the painting in 2007. $ (Round to the nearest dollar.) d) What is the doubling time for the value of the painting to the nearest tenth of a year? years (Round to the nearest tenth.) e) Find the amount of time after which the value of the painting will be $6430. years (Round to the nearest tenth.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Exponential Growth Problem: Estimating the Value of a Painting
In this example, we explore the exponential growth of the value of a painting. A painting sold for $246 in 1980 and was sold again in 1985 for $439. Assuming that the growth in the value \(V\) of the collector's item follows an exponential model, we will answer several questions.
----
**a) Find the value \(k\) of the exponential growth rate. Assume \(V_0 = 246\).**
\[ k = \_ \]
(Round to the nearest thousandth.)
----
**b) Find the exponential growth function in terms of \(t\), where \(t\) is the number of years since 1980.**
\[ V(t) = \_ \]
----
**c) Estimate the value of the painting in 2007.**
\[ \$ \_ \]
(Round to the nearest dollar.)
----
**d) What is the doubling time for the value of the painting to the nearest tenth of a year?**
\[ \_ \, \text{years} \]
(Round to the nearest tenth.)
----
**e) Find the amount of time after which the value of the painting will be $6430.**
\[ \_ \, \text{years} \]
(Round to the nearest tenth.)
----
By following these steps, you can estimate the growth of the value of the painting and understand the implications of exponential growth in similar contexts. Effective use of exponential functions is essential in financial mathematics and various growth-related fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3230e3d-dd38-497e-8c1e-7c1c5570828c%2Fd9e4a6ea-bf8d-4cac-929f-e5f4669f2daa%2Fsl6177_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exponential Growth Problem: Estimating the Value of a Painting
In this example, we explore the exponential growth of the value of a painting. A painting sold for $246 in 1980 and was sold again in 1985 for $439. Assuming that the growth in the value \(V\) of the collector's item follows an exponential model, we will answer several questions.
----
**a) Find the value \(k\) of the exponential growth rate. Assume \(V_0 = 246\).**
\[ k = \_ \]
(Round to the nearest thousandth.)
----
**b) Find the exponential growth function in terms of \(t\), where \(t\) is the number of years since 1980.**
\[ V(t) = \_ \]
----
**c) Estimate the value of the painting in 2007.**
\[ \$ \_ \]
(Round to the nearest dollar.)
----
**d) What is the doubling time for the value of the painting to the nearest tenth of a year?**
\[ \_ \, \text{years} \]
(Round to the nearest tenth.)
----
**e) Find the amount of time after which the value of the painting will be $6430.**
\[ \_ \, \text{years} \]
(Round to the nearest tenth.)
----
By following these steps, you can estimate the growth of the value of the painting and understand the implications of exponential growth in similar contexts. Effective use of exponential functions is essential in financial mathematics and various growth-related fields.
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