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DO NOW
DO NOW
Jack puts $450 in a savings account with an interest rate of 8% per year (compounded once per year). Jack wants to have $500,000 so he can retire. If he doesn't add any more money, how many years will be it before he can retire?
LEARNING TARGET
LEARNING TARGET
I can rewrite exponential expressions in logarithmic form.
I can rewrite exponential expressions in logarithmic form.
I DO
I DO
What is a logarithm?
What is a logarithm?
It's simply another way of looking at (and writing) exponential expressions (or powers)
It's simply another way of looking at (and writing) exponential expressions (or powers)
- Consider the example of 2 to the 5th
- What does it equal?
- 2 is like a growth rate
- 5 is like a time
- 32 is like the final result (how many times bigger you are than when you started)
- 2 to the zero = 1 (same size, no time)
- 2 to the -1 = 1/2 (you're half the size)
Rewrite as logs:
- log2(32)=5
- log2(1)=0
- log2(1/2)=-1
What is log3(81)= ?Rewrite as exponential
A few things to know:
A few things to know:
If the log has no base, the base is 10
There is a special log called the "natural log." This is a log with base "e." We write it as ln.
You're good enough. You're smart enough. And, doggone it, people like you!
let's do some examples:
let's do some examples:
Let's revisit the Do Now problem:
Let's revisit the Do Now problem:
500,000 = 450 ( 1 + .08)^t
500,000 = 450 ( 1 + .08)^t
Can we find t using logarithms?
Can we find t using logarithms?
WE DO
WE DO
YOU DO
YOU DO
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