Properties of Logarithmic Functions notes (day 2) Logarithmic Growth Logarithmic Decay Domain: Domain: Range: Range: Asymptote: Asymptote: EX Use the graph of f(x) = log x and g(x) = ln x to describe the transformation that results in each function. a) log(x + 4)
e) ln x – 2
b) –log x - 5
f) ln (x+4) +3
c) log(x+2)
g) –log (x-2)
d) ln(x-6)
Real World Example: The intensity level of sound, measured in decibels, can be modeled b𝑦 !
𝑑 𝑤 = 10 𝑙𝑜𝑔 ! , where w is the intensity of the sound in watts per square meter and w0 is the !
constant 1.0 x 10-­‐12 watts per square meter. a) If the intensity of the sound of a person talking loudly is 3.16 x 10-­‐8 watts per square meter, what is the intensity level of the sound in decibels? b) If the threshold of hearing for a certain person with hearing loss is 5 decibels, will a sound with an intensity level of 2.1 x 10-­‐12 watts per square meter be audible to that person? Real World Example 2: The number of machines infected by a specific computer virus can be modeled by 𝑐 𝑑 = 6.8 + 20.1 ln 𝑑 , where d is the number of days since the first machine was infected. a) About how many machines were infected on day 12? b) How many more machines were infected on day 30 than day 12?