12. Given: ,f (x)dx = 4 and f, f(x)dx =-1. Find: (b) 13. Suppose P(t) = 0.1575 (1.032)' is rate, measured in millions per year, at which the population of a country is increasing. a) Calculate P(1) dt . b) What are the units of P(t) dt? c) What is the practical meaning of "P(1) dt ? d) Suppose the population is currently 5 mill. What is the population in 10 years?
12. Given: ,f (x)dx = 4 and f, f(x)dx =-1. Find: (b) 13. Suppose P(t) = 0.1575 (1.032)' is rate, measured in millions per year, at which the population of a country is increasing. a) Calculate P(1) dt . b) What are the units of P(t) dt? c) What is the practical meaning of "P(1) dt ? d) Suppose the population is currently 5 mill. What is the population in 10 years?
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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a-d
![**12. Given:**
\[
\int_{0}^{3} f(x) dx = 4 \quad \text{and} \quad \int_{3}^{7} f(x) dx = -1.
\]
Find:
(a) \(\int_{0}^{7} f(x) dx =\)
(b) \(\int_{3}^{7} 2f(x) dx =\)
**13. Suppose** \(P(t) = 0.1575(1.032)^t\) is the rate, measured in millions per year, at which the population of a country is increasing.
a) Calculate \(\int_{0}^{10} P(t) dt \).
b) What are the units of \(\int_{0}^{10} P(t) dt \)?
c) What is the practical meaning of \(\int_{0}^{10} P(t) dt \)?
d) Suppose the population is currently 5 million.
What is the population in 10 years?
---
**Notes:**
- The problem involves calculating definite integrals and understanding their practical implications.
- There are no graphs or diagrams in this image.
- The problem explores integration and growth in the context of population increase, requiring calculation and interpretation of the results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F587f9f8f-b9b6-467a-a476-89151f1449a5%2Fa1d763f0-a72b-450e-ac47-0416e1fbd017%2Fwj0b3n9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**12. Given:**
\[
\int_{0}^{3} f(x) dx = 4 \quad \text{and} \quad \int_{3}^{7} f(x) dx = -1.
\]
Find:
(a) \(\int_{0}^{7} f(x) dx =\)
(b) \(\int_{3}^{7} 2f(x) dx =\)
**13. Suppose** \(P(t) = 0.1575(1.032)^t\) is the rate, measured in millions per year, at which the population of a country is increasing.
a) Calculate \(\int_{0}^{10} P(t) dt \).
b) What are the units of \(\int_{0}^{10} P(t) dt \)?
c) What is the practical meaning of \(\int_{0}^{10} P(t) dt \)?
d) Suppose the population is currently 5 million.
What is the population in 10 years?
---
**Notes:**
- The problem involves calculating definite integrals and understanding their practical implications.
- There are no graphs or diagrams in this image.
- The problem explores integration and growth in the context of population increase, requiring calculation and interpretation of the results.
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