6.1 Exponential Growth/Decay Functions
6.2 The Natural Base e
6.3 Logarithms
6.5 Properties of Logarithms
6.6 Solving Exponential and Logarithmic Equations
100
Determine whether the function represents exponential growth or decay:
y=1/5*2^x
Exponential Growth
100
What is the approximate value of e?
~2.718
100
What is a logarithm?
An exponent!
100
True or False (and explain):
log_b m+log_b n = log_b(m + n)
False
100
log(5x-8)=log(3x-4)
x=2
200
Graph:
y=4*(1/2)^x
200
Simplify:
e^7/e^5
e^2
200
Evaluate:
log_5 1
0
200
True or False (and explain):
log_b m - log_b n = log_b m/(log_b n)
False
200
log_3 (2x-5)=2
x=7
300
You bought a car new for $30,000. The value of your car decays exponentially by 10% each year. Write an equation to model the car's value V after t years.
V(t) = 30,000(0.9)^t
300
Determine whether the function is exponential growth or decay:
y=6e^(-6x)
Exponential Decay
300
Evaluate:
ln(1/e)
-1
300
Expand:
log_8 3x^2y
log_8 3 + 2log_8 x + log_8 y
300
5^(x − 3) = 25^(x − 5)
x=7
400
The average price for a gallon of milk was $1.03 in 1990. Since then, the price has increased approximately 2.7% each year. Find the year in which the cost of a gallon of milk was $1.27.
1998
400
Simplify:
(e^-8e^6)/e^4
1/e^6
400
Evaluate:
log_100(1/10)
-1/2
400
Condense:
ln40+ln3 - ln10
ln 12
400
Solve for x.
log_2 x + log_2(x − 2) = 3
x=4
500
You deposit $1,500 into an account that pays 7% annual interest. Find the balance (to the nearest hundredth) after 10 years when the interest is compounded monthly.
$3,014.49
500
An account earns 3% annual interest compounded continuously. Find the principal (to the nearest hundredth) when the balance is $100 after 10 years.
$74.08
500
Find the inverse of:
y=log(x-7)
y=10^x+7
500
Expand:
log_7 ((a^3b\sqrtc)/(2d))
3log_7 a + log_7 b + 1/2 log_7 c - log_7 2 - log_7 d
or
3log_7 a + log_7 b + 1/2 log_7 c - (log_7 2 + log_7 d)
500
Solve for x. Leave your answer in terms of a logarithm.
5(7)^(5x)-2 = 58
log_7 12/5
or
log12/(5log7)