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.

Here, the given function is: P(t)=2800e0.045t...(1)Let, P=2800e-0.045t⇒e-0.045t=P2800⇒-0.045t=lnP2800⇒t=-10.045lnP2800 So, the function f(P)=-10.045lnP2800 which gives you time as a function of amount P in the account.

Math

Calculus

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...

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