Warm-Up Algebra 2 Honors 2/19/18 Solve the following equations: 1. f(x)=Log (x) when x=23 2. f(x)=Log ( 𝑥 3 ) when x=20 3. f(x)= Log(x) +23 when x=3 4. Log(x)= 2+1.5C when C=4.5 5 to do 5 to go over 10 total

Logarithmic functions NOTES

Finances Chemistry Earthquakes Sound Astronomy Sound- Decibels Earthquakes – Richter Scale Astronomy - Brightness of stars Chemistry – PH scale Finances – Compound Interest 1 minute Sound Astronomy

Earthquakes Richter Scale 𝑅= log ( 𝐴 𝐴 0 ) amplitude The magnitude of an earthquake is related to how much energy is released by the quake. Instruments called seismographs detect movement in the earth; the smallest movement that can be detected shows on a seismograph as a wave with amplitude A0. A – the measure of the amplitude of the earthquake wave A0 – the amplitude of the smallest detectable wave (or standard wave) From this you can find R, the Richter scale measure of the magnitude of the earthquake using the formula: The intensity of an earthquake typically measures between 2 and 10 on the Richter Scale. Below 5 are minor and may shake the ground a bit but rarely cause much damage. Between 5 and 7.9 are much more severe, above an 8 causes massive damage. The highest rating ever recorded for an earthquake is 9.5 during the 1960 Valdivia earthquake in Chile. amplitude The distance between the highest point and the rest position (zero position) in a wave. 𝑅= log ( 𝐴 𝐴 0 ) 4 minutes Total 15 September 2017 the earthquake in Mexico was a 7.1 magnitude and killed over 200 people

𝑅= log ( 𝐴 𝐴 0 ) 2.6 Magnitude Earthquake!! 𝐴=392∗ 𝐴 0 An earthquake is measured with a wave amplitude 392 times as great as A0. What is the magnitude of this earthquake using the Richter scale, to the nearest tenth? 𝑅= log ( 𝐴 𝐴 0 ) Start with the Richter Scale formula Find A Plug it in Simplify Take the log Round to the nearest tenth 2.6 Magnitude Earthquake!! 𝐴=392∗ 𝐴 0 5 minutes Total – 20 minutes 𝑅= log ( 392 𝐴 0 𝐴 0 ) 𝑅= log (392)

Now try an earthquake of 3,920 amplitude 3.6 Magnitude! 3 minutes Total – 23 minutes

On 1/26/18 at 4:31 Am there was an earthquake with an amplitude of 79432823.5 times a standard wave off the coast of Alaska. What was the magnitude of the earthquake? 2 minutes Total 25 minutes 7.9

The magnitude of an earthquake is also related to the energy released in Joules log10 E = 4.4 + 1.5M Recently there was a 3.3 magnitude earthquake in southern California. What was the approximate energy released during this earthquake log10 E = 4.4 + 1.5(3.3) log10 E = 9.35 109.35=E E= 2238721138.57 J 7 minutes 32 minutes

How much energy was released in the 7.2 earthquake on Friday in Mexico? log10 E = 4.4 + 1.5M log10E= 4.4+1.5(7.2) log10E=15.2 1015.2=E E=1.58 x 1015 J 5 minutes 37 minutes

Compound Interest Formula Suppose that a principal of P dollars is invested at an annual interest rate r (in percent, expressed as a decimal), compounded n times per year. Then the amount A accumulated after t years is given by the formula A= the total amount accumulated P=The initial investment r= the ANNUAL interest rate n= how many times it’s compounded every year t= how many years 𝐴=𝑃(1+ 𝑟 𝑛 )nt 3 minutes 40 minutes

Example: Compound Interest Formula Suppose that $2000 dollars is invested at an annual rate of 8%, compounded quarterly. Find the total amount in the account after 6 years if no withdrawals are made. 𝐴=2000(1.02)24 𝐴=𝑃(1+ 𝑟 𝑛 )nt 𝐴=2000(1+ .08 4 )4*6 There would be $3216.88 in the account at the end of six years. 5 minutes 45 minutes 𝐴=2000(1+.02)24

Example: Compound Interest Formula Suppose that $500 dollars is invested at an annual rate of 6%, compounded semi-annually. Find the total amount in the account after 4 years if no withdrawals are made. A=633.385 𝐴=𝑃(1+ 𝑟 𝑛 )nt A=500(1+ .06 2 )2*4 There would be $633.39 in the account at the end of four years. 5 minutes 50 minutes A=500(1.03)8