Question

A college fund is started with an initial deposit of $2,000.00. The amount in the fund after x number of years is represented by the recursive equation
f
(
x
)
=
f
(
x
−
1
)
⋅
1.06
, in which
f
(
0
)
=
2
,
000
. Use this recursive formula to create an exponential equation that models the fund’s balance,
A
, after t years, assuming there were no additional deposits or withdrawals. Which of the following is the correct equation?(1 point)

A
=
2
,
000
⋅
1.06
t

A
=
2
,
000
e
0.06
t

A
=
2
,
000
e
0.058
t

A
=
2
,
000
e
0.061
t

Answer 1

A = 2,000 · 1.06^t

Reason: each year the balance is multiplied by 1.06 (6% annual growth), so after t years A = 2000(1.06)^t.