SOLUTION: A college loan of $44,000 is made at 3% interest, compounded annually. After t years, the amount due, A, is given by the function. A(t) = 44,000 (1.03)^t. After what amount of

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A college loan of $44,000 is made at 3% interest, compounded annually. After t years, the amount due, A, is given by the function. A(t) = 44,000 (1.03)^t. After what amount of       Log On


   



Question 299974: A college loan of $44,000 is made at 3% interest, compounded annually. After t years, the amount due, A, is given by the function.
A(t) = 44,000 (1.03)^t.
After what amount of time will the amount reach $54,000?

Answer by nerdybill(7384) About Me  (Show Source):
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A college loan of $44,000 is made at 3% interest, compounded annually. After t years, the amount due, A, is given by the function.
A(t) = 44,000 (1.03)^t.
After what amount of time will the amount reach $54,000?
.
Simply set A(t) equal to 54000 and solve for t:
A%28t%29+=+44%2C000+%281.03%29%5Et
54000+=+44000+%281.03%29%5Et
54000%2F44000+=+1.03%5Et%0D%0A%7B%7B%7B54%2F44+=+1.03%5Et
log%281.03%2C%2854%2F44%29%29+=+t
log%2854%2F44%29%2Flog%281.03%29%29+=+t
+6.93+=+t+
Rather:
t = 6.93 years