SOLUTION: Suppose that $5000 is invested at interest rate k, compounded continuously, and grows to $6954.84 in 6 years. a) Find the interest rate. b) write the exponential growth function.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Suppose that $5000 is invested at interest rate k, compounded continuously, and grows to $6954.84 in 6 years. a) Find the interest rate. b) write the exponential growth function.       Log On


   

Question 148856This question is from textbook Essentials of College Algebra Alternate Edition
: Suppose that $5000 is invested at interest rate k, compounded continuously, and grows to $6954.84 in 6 years. a) Find the interest rate. b) write the exponential growth function. c) Find the balance after 10years. This question is from textbook Essentials of College Algebra Alternate Edition

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that $5000 is invested at interest rate k, compounded continuously, and grows to $6954.84 in 6 years.
:
The continuous interest equation: A+=+P%28e%5E%28rt%29%29


a) Find the interest rate. (find k)
6954.84+=+5000%28e%5E%286k%29%29
:
e%5E%286k%29 = 6954.84%2F5000
:
e%5E%286k%29 = 1.390968
Find the nat log of both sides
ln%28e%5E%286k%29%29 = ln(1.390968)
ln of e is 1
6k = .330
k = .330%2F6
k = .055 or 5.5% interest
:
Check solution on a calc: enter 5000(e^(.055*6)) = 6954.840
:
:
b) write the exponential growth function.
A+=+P%28e%5E%28rt%29%29
:
:
c) Find the balance after 10years.
on Calc enter: 5000(e^(.055*10)) = 8666.27