Problem 116. Chad deposit $ 2800 in-a CD for tax deduction reasons, and to hopefully be able to buy a car when his eventually gives out. The CD has an annual interest rate of 4.5% that is compounded continuously. We It will take Z036 years saw in Definition 98, that this will give us an exponential growth function of the form P(t) = 2500e0.045«t It will take Z036 years %3D 1. How many years will have elapsed before the CD is worth $7000? for the CD to be worth7000 A-P.e(r+) 0,3979co.8461. log @) 7000~メ0 0.645 92.5=e0.04st log (2.5) lege o.04s:) 8.8431 Tos G) 20.36-t 2. Find an equation for the inverse function that gives the time t as a function of the amount in the account.
Problem 116. Chad deposit $ 2800 in-a CD for tax deduction reasons, and to hopefully be able to buy a car when his eventually gives out. The CD has an annual interest rate of 4.5% that is compounded continuously. We It will take Z036 years saw in Definition 98, that this will give us an exponential growth function of the form P(t) = 2500e0.045«t It will take Z036 years %3D 1. How many years will have elapsed before the CD is worth $7000? for the CD to be worth7000 A-P.e(r+) 0,3979co.8461. log @) 7000~メ0 0.645 92.5=e0.04st log (2.5) lege o.04s:) 8.8431 Tos G) 20.36-t 2. Find an equation for the inverse function that gives the time t as a function of the amount in the account.
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...
Related questions
Question
100%
I need help with question 2 only. Thank you :)
![**Problem 116.** Chad deposits $2800 in a CD for tax deduction reasons, and to hopefully be able to buy a car when he eventually gives out. The CD has an annual interest rate of 4.5% that is compounded continuously. We saw in Definition 98, that this will give us an exponential growth function of the form \( P(t) = 2500e^{0.045t} \).
1. **How many years will have elapsed before the CD is worth $7000?**
- Using the formula \( A = Pe^{(rt)} \), we solve for \( t \):
\[
7000 = 2800e^{0.045t}
\]
\[
\frac{7000}{2800} = e^{0.045t}
\]
\[
2.5 = e^{0.045t}
\]
Taking the natural logarithm:
\[
\log(2.5) = 0.045t \log(e)
\]
\[
t = \frac{\log(2.5)}{0.045}
\]
Solution: \( t \approx 20.36 \) years
- Handwritten calculation confirms: It will take approximately 20.36 years for the CD to be worth $7000.
2. **Find an equation for the inverse function that gives the time \( t \) as a function of the amount in the account.**
- Solve for \( t \) in terms of \( A \):
\[
A = Pe^{(rt)}
\]
\[
\frac{A}{P} = e^{rt}
\]
\[
\log\left(\frac{A}{P}\right) = rt
\]
\[
t = \frac{\log\left(\frac{A}{P}\right)}{r}
\]
**Note:** There are several scribbled calculations on the paper indicating steps to solve for \( t \). Some handwritten notes also attempt to calculate with constants like 0.3979 and 0.645.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a383c1c-55bf-4954-84ad-343efbbae6d4%2F0cd462ea-ad03-402c-bff6-280eee6a2776%2Fyhz7fjdw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 116.** Chad deposits $2800 in a CD for tax deduction reasons, and to hopefully be able to buy a car when he eventually gives out. The CD has an annual interest rate of 4.5% that is compounded continuously. We saw in Definition 98, that this will give us an exponential growth function of the form \( P(t) = 2500e^{0.045t} \).
1. **How many years will have elapsed before the CD is worth $7000?**
- Using the formula \( A = Pe^{(rt)} \), we solve for \( t \):
\[
7000 = 2800e^{0.045t}
\]
\[
\frac{7000}{2800} = e^{0.045t}
\]
\[
2.5 = e^{0.045t}
\]
Taking the natural logarithm:
\[
\log(2.5) = 0.045t \log(e)
\]
\[
t = \frac{\log(2.5)}{0.045}
\]
Solution: \( t \approx 20.36 \) years
- Handwritten calculation confirms: It will take approximately 20.36 years for the CD to be worth $7000.
2. **Find an equation for the inverse function that gives the time \( t \) as a function of the amount in the account.**
- Solve for \( t \) in terms of \( A \):
\[
A = Pe^{(rt)}
\]
\[
\frac{A}{P} = e^{rt}
\]
\[
\log\left(\frac{A}{P}\right) = rt
\]
\[
t = \frac{\log\left(\frac{A}{P}\right)}{r}
\]
**Note:** There are several scribbled calculations on the paper indicating steps to solve for \( t \). Some handwritten notes also attempt to calculate with constants like 0.3979 and 0.645.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning