A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2008, can be approximated by V(t) = 1.3 e 0.0411 where t=0 corresponds to 2008 and V is in billions of dollars. a) Estimate the value of the country's exports in 2008 and 2020. b) What is the doubling time for the value of the country's exports?

A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2008, can be approximated by V(t) = 1.3 e 0.0411 where t=0 corresponds to 2008 and V is in billions of dollars. a) Estimate the value of the country's exports in 2008 and 2020. b) What is the doubling time for the value of the country's exports?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Interpret the first and second derivatives graphically.
%3D
%3D
3D
Drag each of the above graphs of continuous functions into the appropriate area below so that each segment of the graph, separated by a dashed line, matches the signs of f' and f''.
f'
+
+
+
+
+
+
f'"
+
+
+

0.041t
A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2008, can be approximated by V(t) = 1.3 e
where t= 0 corresponds to 2008 and V is in billions of dollars.
%3D
a) Estimate the value of the country's exports in 2008 and 2020.
b) What is the doubling time for the value of the country's exports?
a) The value of the country's exports in 2008 is $
(Simplify your answer. Round to the nearest tenth as needed. Do not include the $ symbol in your answer.)
billion.
The value of the country's exports in 2020 is $
(Simplify your answer. Round to the nearest tenth as needed. Do not include the $ symbol in your answer.)
billion.
b) The doubling time is approximately
years.
(Simplify your answer. Round to the nearest integer as needed.)

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