Student Goals:
Students will be able to understand the difference between the growth and decay of a function.
Exponential Growth:
When defining exponential growth, we can take the formula
Let's go ahead and look at an example to see an exponential growth. So, this is a basic example of using the formula of y=(2)^x.
Now, let's look at a real life word problem.
Amanda has $300 in a saving account that earns a 10% interest, compounded annually. To the nearest cent, how much will she earn in 4 years?
I know word problems can seem challenging, but let's go ahead and break it down and see what each number represents.
Amanda has $300 in her account, so this will represent the starting amount, which we will call p.
The interest earned is 10%. To turn this into a decimal, we simply move the decimal over 2 times from where the % is. In this case the number will be 0.10 where we will label it as r.
Now we look at in how much time they want us to look for, which is 4 years and will have the label t.
I have all the information that I need so I can now put it all together.
Compound Interest
This is when the bank pays interest on the initial principle and the interest an account has already earned, the bank is paying compound interest.
Exponential Decay
With exponential decay, the formula is different, because instead of adding we are subtracting the percentage rate.
