Question
upstudy study bank question image url

On January 2,2006 , Jorge Sanchez deposited \( \$ 450 \) into a savings account that pays simple interest at a rate of \( \$ 12 \) each year. The amount in the account is a function of time given by \( A(t)=450+12 t \), where \( t \) is the number of years after 2006. Find the amount in the account in a) 2007, b) 2018 . a) The amount in the account in 2007 will be \( \$ \square \). b) The amount in the account in 2018 will be \( \$ \square \).

Ask by Hart Cervantes. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

a) \$462 b) \$594

Solution

**Step 1: Identify the formula** We are given the function for the amount in the account as \[ A(t) = 450 + 12t, \] where \( t \) is the number of years after 2006. **Step 2: Calculate the amount for 2007** For the year 2007, \[ t = 2007 - 2006 = 1. \] Plug \( t = 1 \) into the function: \[ A(1) = 450 + 12(1) = 450 + 12 = 462. \] Thus, the amount in the account in 2007 is \$462. **Step 3: Calculate the amount for 2018** For the year 2018, \[ t = 2018 - 2006 = 12. \] Plug \( t = 12 \) into the function: \[ A(12) = 450 + 12(12) = 450 + 144 = 594. \] Thus, the amount in the account in 2018 is \$594. a) The amount in the account in 2007 will be \$462. b) The amount in the account in 2018 will be \$594.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Bonus Knowledge

To find the amount in the account for the given years, we can substitute the values of \(t\) into the function \(A(t) = 450 + 12t\). a) For the year 2007, \(t = 1\) (since 2007 is one year after 2006): \[ A(1) = 450 + 12(1) = 450 + 12 = 462 \] So, the amount in the account in 2007 will be \( \$ 462 \). b) For the year 2018, \(t = 12\) (since 2018 is twelve years after 2006): \[ A(12) = 450 + 12(12) = 450 + 144 = 594 \] Therefore, the amount in the account in 2018 will be \( \$ 594 \).

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy