Question

A high-yield savings account that compounds interest continuously was opened in 1991. The recursive equation
f
(
x
)
≈
f
(
x
−
1
)
⋅
1.375
shows the amount of money in the account rounded to the nearest cent for each year after 2000, in which
f
(
0
)
=
3
,
500
. Use the recursive formula to create an exponential equation that models the account’s balance,
A
, after t years, assuming there were no withdrawals or deposits. What is the correct equation, with r rounded to three decimal places and
P
rounded to two decimal places? While solving, round values to three decimal places. (1 point)

A
=
3
,
500
e
0.318
t

A
=
3
,
500
e
0.375
t

A
=
3
,
500
(
1.318
)
t

A
=
3
,
500
(
1.375
)
t

Answer 1

We need r with e^r = 1.375, so r = ln(1.375) ≈ 0.318 (to three decimals). P = f(0) = 3500 → 3500.00 (two decimals).

Thus A = 3500.00 e^{0.318 t}, i.e. A = 3500 e^{0.318t}.