Applications of Exponential Functions

Hey guys, it's Mark. Today we had our final lesson for the unit Exponents & Logarithms. Mr P showed us how to use exponents and logarithm functions in real life situations. We were given formulas for growth and decay, compound interest and, continuous compound interest.

In the upcoming formulas you will see will have the same meanings to the variables. Those are :
A = Final amount
P = Initial amount
e = The constant "e" (on your calculator)
r = Rate/constant
t = Time


The first formula was : Growth and Decay

That formula is -


The second formula was : Compound Interest

That formula is -

The third formula was : Continuous Compound interest


That formula is -

Did this one seem familiar? It's because it's the same as the first one :P

Example:
I will use the second question from the handout.
The temperature, T, in degrees Celsius, of a cup of coffee t minutes after it is poured is given by .
a. How hot was the coffee when it was first poured?
b. Find the temperature of the coffee 10 minutes later.

The first question is straight up. It asks us for the initial temperature which is 95.

To find b, we have to plug in 10 into the formula. It then becomes :
All we have to do now is plug it into our calculators. The answer i got was (57.6).

This should be easy for most of us, there will be one question like this on the provincial exam.

For those who didn't see my scribe last year, I made a funny.
(: