Algebra 2 Help? [Lesson Entitled: Graphs of Exponential Functions]?

Question

I'm not sure what to do, and the instructions are as followed:

"BANKING - Find the doubling time of money in a bank account earning interest compounded annually at each interest rate. Round each doubling time to the nearest whole number of years

1. 8%
2. 6%
3. 4%
4. 9%
5. 12%
6. 18%"

You don't have to do all of them, but if you would, would you do one and explain it to me?

Thanks in advance. :D

Answer 1

Since this is for an algebra course, you're probabvly supposed to use the compound interest formula. The basic formula for annual compound interest is A = P(1 + i)^t, where A is the final amount, P is the principal, i is the rate of interest (as a decimal), and t is the number of years (which is what you're solving for). For "doubling", P is always 1 and A is always 2. So the first problem would be 2 = 1(1+.08)^t or 2 = 1.08^t. You solve this using logarithms. If you have a calculator where you can see what you type on the screen, enter log(2) / log(1.08). If you have an cheaper scientific calculator, you may enter it backwards ... 2 log / 1.08 log . The answer is about 9.006458, or just over 9 years.

A lot of business courses instead of using the compound interest formula use what's called the "rule of 72" to find doubling times. With that you just take the number 72 divided by the interest rate. So for 8%, you'd take 72 / 8 = 9 years. This gives a pretty good estimate (though not the exact answer) for doubling times.

Answer 2

confident, I accept as true with the votes that it is a undesirable question. Logarithms and exponentials are inverse purposes. Graph them by using utilising reflecting them over the graph of y=x. Ask you instructor for extra explanation, too. Your coach will on the brink of likely ought to make the relaionships between logarithmic and exponential centers extra sparkling to you than your contemporary expertise. good success! :)