The amount of money invested in a certain account increases according to the following function, where yo is the initial amount amount present at time t (in years). 0.0225t y=yoe After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answe years X
The amount of money invested in a certain account increases according to the following function, where yo is the initial amount amount present at time t (in years). 0.0225t y=yoe After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answe years X
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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![### Investment Growth and Doubling Time
#### Understanding Investment Growth
The amount of money invested in a certain account increases according to the following exponential function:
$$ y = y_0 e^{0.0225t} $$
where:
- \( y \) is the amount present at time \( t \) (in years),
- \( y_0 \) is the initial amount invested,
- \( e \) is the base of the natural logarithm,
- \( 0.0225 \) is the rate of growth per year.
#### Problem Statement
After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answer to the nearest year.
[Input box for years]
[end of input box]
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##### Explanation of Diagrams (if any)
There are no graphs or diagrams in the displayed image.
---
This textual content is suitable for inclusion on an educational website to aid in the comprehension of exponential growth in investments. Here, students are required to solve for the time it takes for an initial investment to double based on the given growth formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbae73a37-719e-4892-8745-1f816a181ea7%2F12b20125-1cd2-4346-9967-5482d2b4592a%2Fn218pdl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Investment Growth and Doubling Time
#### Understanding Investment Growth
The amount of money invested in a certain account increases according to the following exponential function:
$$ y = y_0 e^{0.0225t} $$
where:
- \( y \) is the amount present at time \( t \) (in years),
- \( y_0 \) is the initial amount invested,
- \( e \) is the base of the natural logarithm,
- \( 0.0225 \) is the rate of growth per year.
#### Problem Statement
After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answer to the nearest year.
[Input box for years]
[end of input box]
[Continue button]
##### Explanation of Diagrams (if any)
There are no graphs or diagrams in the displayed image.
---
This textual content is suitable for inclusion on an educational website to aid in the comprehension of exponential growth in investments. Here, students are required to solve for the time it takes for an initial investment to double based on the given growth formula.
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