Question
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.
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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 \( \$ 594 \).
