SOLUTION: Someone please help me with the following problem: Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years. (a) Find the intere

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Someone please help me with the following problem: Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years. (a) Find the intere      Log On


   

Question 169194: Someone please help me with the following problem:
Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years.
(a) Find the interest rate

(b) Find the exponential growth function



(c) Find the balance after 10 years



(d) Find the doubling time


Thanks.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Someone please help me with the following problem:
Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years.
:
The continuous interest formula: P%2Ae%5E%28rt%29 = A
Where:
P = initial amt (5000)
r = interest rate in decimal form (k in this problem)
t = time, in years (6yrs)
A = final amt (6954.84)
:
(a) Find the interest rate
5000%2Ae%5E%286k%29 = 6954.84
e%5E%286k%29 = 6954.84%2F5000
:
e%5E%286k%29 = 1.390968; divided both sides by 5000
:
6k*ln(e) = ln(1.390968); find the nat log of both sides
:
6k = .33; nat log of e is 1
:
k = .33%2F6
k = .055, 5.5% interest
:
Check on a calc: enter: 5000*e^(6*.055) = 6954.84
>
:
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(b) Find the exponential growth function
A = 5000%2Ae%5E%28.055t%29
;
:
(c) Find the balance after 10 years
On a calc enter 5000%2Ae%5E%28%28.055%2A10%29%29 = 8666.27


(d) Find the doubling time
5000%2Ae%5E%28.055t%29 = 10000; we want to find t here
:
e%5E%28.055t%29 = 10000%2F5000
:
e%5E%28.055%29 = 2;
:
.055t*ln(e) = ln(2); find the nat log of both sides
:
.055t = .693;
:
t = .693%2F.055
t = 12.6 yrs
:
:
Check on a calc: enter: 5000*e^(12.6*.055) = 9998.53 ~ 10000
>