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Logs formula

Cn = Co (1+i) ^ t 

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Logs | Notes

Level 1: Coverting Exponential - Logarithmic 

(What is the exponent on base to get answer?)

Ex: 2^10 (1024) <-> log 2 (1024) = 10

Level 2: Logarithmic - Exponential 

Ex: log3 (243) = 5 <-> 3^5 = 243 

Level 3: Change of base rule 

Ex: 

log3 243 = b <-> 

log10 243

————— = b

log10 3

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Exponential Growth | Notes

Google sheets: 1 (= above x 2)

- X = time

- Y = Original Amount

- Increasing by 5% -> 0.05

- To the power of X -> time 

Ex: 1000 (1 + 0.05)^t

Exponential Function: 

Cn = Co( 1 + i ) ᵗ

- Cn = Final Value

- Co = Initial Value

- i = growth rate (% as a decimal)

- t = time

Example Video:

Cn =  9652 ( 1 + 0.056 )⁸

Cn =  9652 ( 1.056 )⁸

Cn = 14925.4921

Cn =  14925

14925 mice after 8 days. 

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Rational Exponents | Notes

- n does not exist if a is negative and n is even.

- Formula: a^1/n = n (square root) a

- Square root if -1 is I 

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First Math Blog | Talia Salis

Imagination Project:

A) 1. Digitally design a clothing piece of your choosing by solving formulas that consist of algebra, systems of equations, analytical geometry, etc... 

A) 2. Complete one really big problem solving question that involves multiple ways of finding the right answer.

A) 3. Draw/ paint a picture using the “connect the dots” strategy by solving multiple mathematical formulas.

B) 1. I hope I will learn how to become more of an independent student/ learner, and hope to complete assignments without excessive amounts of help. 

C) 1. I do not feel comfortable with ratios and have a lot of difficulty with similar triangles. I fear that I will not be able to complete homework on time, or that I will not be able to keep up with the speed of the workload and class work.