Answer:
Exponential Function: [tex]A= P* e ^ {0.061t}[/tex]
Balance after
t=1 $ 13,524.32
t=2 $ 14,374.99
t=5 $ 17,261.69
t=10 $ 23,417.64
Step-by-step explanation:
Formula used to find amount in the account after time t, given the interest rate is compounded continuously
[tex]A= Pe^r^t[/tex]
where: P= principal amount or amount invested
r= interest rate
t= time
A= amount after time t
in our question we are given:
P=$12,724
r= 6.1% or 0.061
[tex]A= 12724 * e ^ (^0^.^0^6^1^)^t[/tex]
The above equation is exponential function that describes the amount in the account after time t in years
Now, for t = 1
[tex]A= 12724 * e ^ {0.061 * 1}[/tex]
A= $ 13,524.32
t=2
[tex]A= 12724 * e ^ {0.061 * 2}[/tex]
A= $ 14,374.99
t= 5
[tex]A= 12724 * e ^ {0.061 * 5}[/tex]
A= $ 17,261.69
t=10
[tex]A= 12724 * e ^ {0.061 * 10}[/tex]
A= $ 23,417.64
