Prepared: Thu Apr 22 15:37:50 CDT 1999

MATH 1151

Quiz III

1) Solve the following equations:
a)
The equivalent expression in exponential form is

Multiply both sides by 10 and then take cube root to get

b)

Here use the property that logarithm is a one-to-one function.

But if we pick up , then will not be defined. So the only solution is .

2) Use the properties of the logarithm to expand

3) a) Express in exponential form:

b) Express in logarithmic form:

Note: These convertions should be obvious. But if you are still having trouble, you might want to try the following trick:
Base of logarithm becomes base in the exponent and vice versa. So, for example in the first equation, 7, the base of the logarithm, becomes the base for the exponent.

But this is not all. For the rest, the only thing you need to make sure that the exponential form should look different than the logarithmic form. So it is NOT but rather which is obviously different than the logarithmic form. Try this method for different equations.

4) Is it better to invest at 8% compounded quarterly or 7.75% compounded continuously?

The investment formula for interest compounded n times with annual interest rate r is

So $100 in the first plan will become

after one year.

When an interest is compounded continuously, we use the growth function model to find the balance with interest rate r.

So $100 in the second plan will become

after one year.

Obviously the first plan is better since the balance is larger.