Exponential Functions and the Natural Base e
What is the approximate value of e?
~2.718
Bonus: What is an alternative name for e (other than "the natural base)?
Fill in the blanks:
A common logarithm is a logarithm with base ___. A _____ logarithm is a logarithm with base e.
10; natural
State the names of the three logarithmic properties
Product, Quotient, and Power
Solve ln(5x + 2) = ln(x + 10)
x = 2
Evaluate 642/3 without a calculator
16
Bonus: Write 642/3 another way
Tell whether the function is exponential growth or decay: y = (4.25)x
Explain your reasoning.
Exponential growth; the base is greater than 1
Rewrite the exponential equation in logarithmic form:
163/4 = 8
log168 = 3/4
True or false:
log613 = log 13/log 6 = ln 13/ ln 6
True
x = -1
State the domain and range of the parent square root function.
Domain: x >= 0
Range: y >= 0
Bonus: State the domain and range of a cube root function
The value of a car can be approximated by the model y = 25(0.9)t. Identify the percent decrease in the value of the car.
10%
Rewrite the logarithmic equation in exponential form:
log381 = 4
34 = 81
Use the change of base formula to evaluate log219
4.248
Solve 2x < 36
x < 5.170
Simplify 2*sqrt(48) - sqrt(3)
7*sqrt(3)
Simplify the expression: (5e4x)3
125e12x
Evaluate log8(1/512) without a calculator
-3
Condense log 6 + 4 log 3 - log 3
log 162
Solve log66x + log6(x - 1) = 2
x = 3
Solve 5*sqrt(x-3) - 2 = 13
x = 12
You deposit $100 in an account that pays 6% annual interest. If the interest is compounded continuously, how long will it take for the balance to reach $1000?
38.38 years
Simplify log327x
3x
Expand ln (5/12x)
ln 5 - ln 12 - ln x
The amount y of oil collected by a petroleum company drilling on the U.S. continental shelf can be modeled by y = 12.263 ln x - 45.381, where y is measured in billions of barrels and x is the number of wells drilled. About how many wells are drilled to fill up 40 billion barrels of oil?
1056 wells
A football player jumps to catch a pass. The maximum heigh h (in feet) of the player above the ground is given by the function h = 1/64* s2, where s is the initial speed (in feet per second) of the player. Find the initial speed of a player who jumps 3 feet in the air to make a catch.
about 13.9 ft/sec