SOLUTION: during one year,the cost of tuition,room,and board at a state university increased 5%.if the cost continues to increase at the rate of 5% per year,how long will it take for the cos
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Question 230213: during one year,the cost of tuition,room,and board at a state university increased 5%.if the cost continues to increase at the rate of 5% per year,how long will it take for the cost of tuition,room,and board to double?round your answer to the nearest year.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
What you need to solve is
^t)
for 
Now this is a rather complex calculation involving logarithms. But a much simpler way to do it is to approximate the answer using the rule of 72. The approximation will be close enough because you are rounding to the nearest year.
Simply divide 72 by the interest rate in percent. 72 divided by 5 is 14.4. Rounded to the nearest year is 14.
By the way, a much closer approximation, using logarithms, comes out to 14.21 -- which also rounds to 14. Here is the log way to do it:
Divide out the original cost, 
.
^t)
Take the log of both sides (you can use base 10 or natural, it doesn't matter)
\ =\ \ln\left((1.05)^t\right))
Use the laws of logs:
\ =\ t\ln(1.05))
}{ln(1.05)})
Now break out the calculator to discover that
John
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