The values, in dollars, of two accounts over time are modeled by
A_1 (t)=6,500× 〖 1.05 〗 ^t
and
A_2 (t)=3,000× 〖 0.96 〗 ^t
The variable tis measured in years.
What is the difference between the accounts after 3 years?
The value of Account 1 is about $4,870less than the value of Account 2.
The value of Account 1 is about $2,654less than the value of Account 2.
The value of Account 1 is about $4,870greater than the value of Account 2.
The value of Account 1 is about $2,654greater than the value of Account 2.
We need to compare the two account values after:
t=3
First, find the value of Account 1:
A_1 (3)=6,500× 〖 1.05 〗 ^3
A_1 (3)=6,500×1.157625
A_1 (3)≈7,524.56
Now find the value of Account 2:
A_2 (3)=3,000× 〖 0.96 〗 ^3
A_2 (3)=3,000×0.884736
A_2 (3)≈2,654.21
Now subtract:
7,524.56-2,654.21=4,870.35
So Account 1 is about:
$4,870
greater than Account 2 after 3 years.
Therefore, the correct answer is:
▭ ( " C " )
Submit