Fascinating Exponential Functions. Lethargic Log Functions. Egotistical Properties Of Logs. Outrageous Exponential & Log Equations. Amazing Exponential & Log Models. 1pt. 1 pt. 1 pt. 1pt. 1 pt. 2 pt. 2 pt. 2pt. 2pt. 2 pt. 3 pt. 3 pt. 3 pt. 3 pt. 3 pt. 4 pt.
& Log Models
f(x) = 3.4x
When x = 5.6
f(x) = 2x-1
Graph f(x) = 2ex – 2 + 4
e2x – 1 = e4
rate of 3% for 20 years
Compounded both monthly and continuously.
What is $4555.30 compounded continuously?
What is 82/3 = 4
e2 = 7.3890….
horizontal asymptotes of the logarithmic function and sketch its graph.
f(x) = ln(3-x)
log (5x + 3) = log 12
and natural logs
log 2.6 x
What is log x
What is ln x
Find the exact value of the logarithmic expression without using a calculator.
What is-0.8? using a calculator.
Use the properties of logarithms to expand the expression as a sum, difference, and /or constant multiple of logarithms.
Ln 4x3(x2 -4)
What is 3/4lnx +1/4[ln(x+2) + ln(x-2)] a sum, difference, and /or constant multiple of logarithms.
¼[3lnx + ln(x + 2) + ln (x – 2)]
½ [log (x + 1) + 2 log (x – 1)] + 6 log x
What is log [x quantity.6(x – 1)x + 1 ]
Solve for x quantity.
ln x = -7
What is e quantity.-7≈ .000912
Solve the exponential equation quantity.
6(23x – 1) – 7 = 9
What is 0.805 quantity.
Solve for x quantity.
e0.125x – 8 = 0
What is 16.6355? quantity.
log 4x – log (12 +x) = 2
What is quantity.1225 + 125 75≈ 1146.500
The number of endangered animal species in the US from 1990 to 2002 can be modeled by
Y = -119 + 164ln t , 10 ≤ t ≤ 22
Where t represent the year, with t = 10 corresponding to 1990. During which year did the number of endangered animal species reach 357?
What is t = 18, which makes the year 1998. to 2002 can be modeled by
How long will it take an initial investment of $600 at a rate of 4.5% to double if compounded quarterly?
What is 1.2965 years? rate of 4.5% to double if compounded quarterly?
Determine the rate at which $1000 will double compounded continuously over 3 years.
What is 23.1%? continuously over 3 years.
The number y of hits a new search engine website receives each month can be modeled by y = 4080 ekt where t represents the number of months the website has been operating. In the websites’s third month, there were 10,000 hits. Find the value of k, and use this result to predict the number of hits the website will receive after 24 months.
What is k = 0.2988 which is appox. 5,309,734 hits? each month can be modeled by y = 4080 e
The number N of bacteria in a culture is modeled by each month can be modeled by y = 4080 e
N = 100ekt
Where t is the time in hours. If N = 300 when t = 5, estimate the time required for the population to double in size.
What is 3.15 hours? each month can be modeled by y = 4080 e
Find the exponential model each month can be modeled by y = 4080 e
y = aebx
that fits the points (0, 1) and (3, 10)
What is y = e each month can be modeled by y = 4080 e0.7675x