August 2023 Algebra 2 Regents Part IV

This exam was adminstered in August 2023.

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Algebra 2 August 2023

Part IV: A correct answer will receive 6 credits. Partial credit can be earned. One computational mistake will lose 1 point. A conceptual error will generally lose 2 points (unless the rubric states otherwise). It is sometimes possible to get 1 point for a correct answer with no correct work shown.


37.The Manford family started savings accounts for their twins, Abby and Brett, on the day they were born. They invested $8000 in an account for each child. Abby’s account pays 4.2% annual interest compounded quarterly. Brett’s account pays 3.9% annual interest compounded continuously. Write a function, A(t), for Abby’s account and a function, B(t), for Brett’s account that calculates the value of each account after t years.

Determine who will have more money in their account when the twins turn 18 years old, and find the difference in the amounts in the accounts to the nearest cent.

Algebraically determine, to the nearest tenth of a year, how long it takes for Brett’s account to triple in value.

Answer:

A is an exponential growth function. B is continuously compounded and uses e instead.

A(t) = 8000(1 + .042/4)^4t
B(t) = 8000e^.039t

For the second part, evaluate both functions for t = 18:

A(18) = 8000(1 + .042/4)⁴⁽¹⁸⁾ = 16970.899 = $16,970.90

B(18) = 8000e^.039(18) = 16142.273 = $16,142.27

The difference in the accounts will be 16970.90 - 16142.27 = $828.63.

To find when Brett's will triple in value, we need to find when B(t) = 24000.

8000e^.039t = 24000
e^.039t = 24000/8000
ln(e^.039t) = ln(24000/8000)
.039t = 1.09861...
t = 28.1695...

In 28.2 years the value in Brett's account will triple.

End of Exam

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