SOLUTION: A college loan of $30,000 is made at 8% interest compounded annually. After t years,the amount due,A,is given by the function A (t)=30,000 (1.08)^t a)After what amount of time wil

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A college loan of $30,000 is made at 8% interest compounded annually. After t years,the amount due,A,is given by the function A (t)=30,000 (1.08)^t a)After what amount of time wil      Log On


   

Question 419387: A college loan of $30,000 is made at 8% interest compounded annually. After t years,the amount due,A,is given by the function A (t)=30,000 (1.08)^t
a)After what amount of time will the amount due reach $45,000?
t= years
Thank you ,
Debbie
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+%28t%29=30000%2A%281.08%29%5Et+
+45000+=+30000%2A%281.08%29%5Et+
Divide both sides by 30000
+1.5+=+%281.08%29%5Et+
Take the log of both sides
+log%281.5%29+=+log%281.08%5Et%29+
Now use the general rule:
log%28a%5Eb%29+=+b%2Alog%28a%29+
+log%281.5%29+=+t%2Alog%281.08%29+
Divide both sides by log%281.08%29
+t+=+log%281.5%29%2Flog%281.08%29+
+t+=+.1761%2F.03342+
+t+=+5.269+
To find months, .269 yrs x 12 months/yr = 3.228
So far I have 5 yrs 3.228 months
To find days, .228 months x 30 days/month = 6.84
So, the time is 5 years, 3 months, 7 days
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check the answer:
+45000+=+30000%2A%281.08%29%5E5.269+
1.5+=+1.50006 (by my calculator)
close enough