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<— x — Unit 🍎 —>

Unit 10: Part 5

*for more [Graphing Logs]

Application Problem

Graph —> Eq

Page 32

#precalc #pc1u6 #exponent graph #natural log #solving natural log

<— x —>

Unit 10: Part 4

Application Problems

*each pic own problem

Exponents

Investment exponent problem

Increase of 1.35% interest per year

f(x) = a(1.0135)^x

Or a(1 + 0.0135)^x

Compound Interest

Always simplify the (1 + r/n) part

Will lose credit otherwise if equation is an answer

Exponent Normal

Exponent e^x

-Half Life

Newton’s Cucking Law of Cooling

Be very aggressive in labelling

It may look like this..

Or it may decide it wants to stab you and look like this

Key:

Determine known variables

Whatever is left is unknown

Unlike with Decibel and Richter test, you don’t need to keep 2 different equations in your head.

Think: PROCESS OF ELIMINATION

LOGS

Richter and Decibel (Lv2)

Richter Scale

2 things in mind

It’s a hot mess.

Remain calm, it’s like any other new equation. This takes time to sort out. Then you’re like AHA!

Note: 10^-4 on bottom

Variables set up:

Example 1: know mag, want strength ratio

m (sub 1) = magnitude of ocean

m (sub 2) = magnitude of city

I (sub 1) = intensity of ocean ??

I (sub 2) = intensity of city ???

Strengh ratio = ???

Equation: Richter scale and..

ratio of strength =

I (sub 1) / I (sub 2)

Strategy:

Want: strength ratio

Problem: no intensity #’s

Solution: solve for intensity

Later: solve for strength ratio

Example 2: know 1 mag + strength ratio, want other mag

m (sub 1) = magnitude of ocean ???

m (sub 2) = magnitude of city

I (sub 1) intensity of ocean ???

I (sub 2) intensity of city ???

strength ratio = #

Equations used: same + …

I (sub 2) = I (sub 1) * strength ratio

Then solve for m (sub 2) with that

Aka. Solve for easy stuff the work up

Solve for magnitude

Decibel

Example 1: 2 diff decibels, want ratio of intensity

B (sub 1) = sound of drill

B (sub 2) = sound of whisper

I (sub 1) = intensity of drill ??

I (sub 2) = intensity of whisper ??

Strength ratio = ???

Equation: normal one

Strength ratio = B[1] / B [2]

Strategy: Similar to richter scale

Think: what do I want

Then: what’s in my way

Last: how do I get past it

These are multi part problems that look overwelhming at first seeing all the missing variables. The key is solve what’s easy, then try the tricky stuff. Sometimes you can bs your way through these problems.

Note: 10^-12 is good for helping you find the intensity.

Note: solve what variables you can before popping in numbers.

Page 31

#precalc #pc1u6 #logs #exponent #solving exponents #solving logs #application problem #richter scale #newton’s law of cooling #decibel #continuous growth #compound interest

Ways to Solve: Logs and Exponents

For the 3rd black box, go to expanding expanding logs to see it solved

Unsolvable Algebraically

#precalc #pc1u6 #logs #exponents #solving logs #solving exponents

Expanding Logs

Combining Logs

#precalc #pc1u6 #logs #solving logs

Log and Exponent Rule Review

#precalc #pc1u6 #logs #exponents

<— x —>

Unit 10: Part 4

Application Problems

*each pic own problem

Exponents

Investment exponent problem

Increase of 1.35% interest per year

f(x) = a(1.0135)^x

Or a(1 + 0.0135)^x

Compound Interest

Always simplify the (1 + r/n) part

Will lose credit otherwise if equation is an answer

Exponent Normal

Exponent e^x

-Half Life

Newton’s Cucking Law of Cooling

Be very aggressive in labelling

It may look like this..

Or it may decide it wants to stab you and look like this

Key:

Determine known variables

Whatever is left is unknown

Unlike with Decibel and Richter test, you don’t need to keep 2 different equations in your head.

Think: PROCESS OF ELIMINATION

LOGS

Richter and Decibel (Lv2)

Richter Scale

2 things in mind

It’s a hot mess.

Remain calm, it’s like any other new equation. This takes time to sort out. Then you’re like AHA!

Note: 10^-4 on bottom

Variables set up:

Example 1: know mag, want strength ratio

m (sub 1) = magnitude of ocean

m (sub 2) = magnitude of city

I (sub 1) = intensity of ocean ??

I (sub 2) = intensity of city ???

Strengh ratio = ???

Equation: Richter scale and..

ratio of strength =

I (sub 1) / I (sub 2)

Strategy:

Want: strength ratio

Problem: no intensity #’s

Solution: solve for intensity

Later: solve for strength ratio

Example 2: know 1 mag + strength ratio, want other mag

m (sub 1) = magnitude of ocean ???

m (sub 2) = magnitude of city

I (sub 1) intensity of ocean ???

I (sub 2) intensity of city ???

strength ratio = #

Equations used: same + …

I (sub 2) = I (sub 1) * strength ratio

Then solve for m (sub 2) with that

Aka. Solve for easy stuff the work up

Solve for magnitude

Decibel

Example 1: 2 diff decibels, want ratio of intensity

B (sub 1) = sound of drill

B (sub 2) = sound of whisper

I (sub 1) = intensity of drill ??

I (sub 2) = intensity of whisper ??

Strength ratio = ???

Equation: normal one

Strength ratio = B[1] / B [2]

Strategy: Similar to richter scale

Think: what do I want

Then: what’s in my way

Last: how do I get past it

Note: 10^-12 is good for helping you find the intensity.

Note: solve what variables you can before popping in numbers.

Page 31

#precalc #pc1u6 #logs #exponent #solving exponents #solving logs #application problem #richter scale #newton’s law of cooling #decibel #continuous growth #compound interest

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