4.1: Inverse Functions
4.2: Exponential Functions
4.3: Logarithmic Functions
4.4: Evaluating Logarithms & Change of Base Theorems
4.5: Exponential & Logarithmic Equations
100
Determine whether or not the function is one-to-one. f(x) = x^2 - 2
No
100
Let f(x) = (1/4)^x. Find f(3).
1/64
100
Write in logarithmic form. 6^2 = 36
logbase(6)of(36) = 2
100
If f(x) = logbase7 (x), find f(7^3).
3
100
Solve the equation. Round to the nearest thousandth. 2e^(5x+3) = 8
{0.877}
200
Use the definition of inverses to determine whether f and g are inverses of each other. f(x) = 3x - 1 and g(x) = (x + 1)/3
Yusssss
200
Let f(x) = 4^x. Find f(5/2)
32
200
Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. logbase(a)of((4x^3)y)
logbase(a)of(4) + 3logbase(a)of(x) + log base(a)of(y)
200
log(683/363) (Calculator allowed)
0.2745
200
Solve the equation. Give the answer in exact form. e^(2x) - 8e^x + 12 = 0
{ln 2, ln 6}
300
Let f(x) compute the time in hours to travel x miles at 25 miles per hour. What does f^-1(x) compute?
The miles traveled in x hours at 25 miles per hour
300
2^(8-2x) = 4
x = 3
300
Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. 3logbase(m)of(y-7) * logbase(m)of(x^2)
logbase(m)of(x^2/y^21)
300
Let u = ln a and v = ln b. Write the following expression in terms of u and v without using the function ln. ln a^7/b^2
7u - 2v
300
Solve for the indicated variable. I = (Io)e^(kt/900), for t
t = (900/k)*ln(I/Io)
400
Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem. The function defined by f(x) = x + 2 was used to encode a message as: 15 3 22 10 9 7 16 11 23 21 Find the inverse function and use that to determine the message.
f^-1(x) = x-2; MATH GENIUS
400
9 = b^2/5
b = {-243,243}
400
Solve: logbase(2)of(x+3) = 5
x=29
400
An earthquake was recorded with an intensity which was 1,258,925 times more powerful than a reference level earthquake, or 1,258,925 * Io. What is the magnitude of this earthquake on the Richter scale (rounded to the nearest tenth)? Intensity on the Richter scale is log(I/Io). (Calculator allowed)
6.1
400
Use your graphing calculator to find how long it will take for $8000 invested at 4.8% per year compounded daily to triple in value. Find the answer to the nearest year. Use 365 days for a year.
23 Years
500
Find the parameters a and b included in the linear function f(x) = a x + b so that f^-1(2) = 3 and f^-1(-3) = 6, where f^-1(x) is the inverse of function f.
a = (-5 /3) and b = 7
500
32^(x-4) = 8^4x
x = -20/7
500
Given log(10)of(2) = 0.3010 & log(10)of(7) = 0.8451, find log(10)of(14) W/OUT A CALCULATOR
log(10)of(14) = 1.1461
500
Quail are game birds that fare poorly when their habitat is encroached upon. Wildlife biologists have discovered that the population P of quail in a region is related to the percent of the region that has been paved with roads and parking lots, according to the formula P = k ln(30/(x+5)), 0 ≤ x ≤ 25, where x is the percent of the region that has been paved. For a particular rural region, P = 1600 when x = 0. Predict what the quail population will be in this region when it becomes 5% paved. Round your answer to the nearest whole number. (Calculator allowed)
981 quail
500
The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^(0.05t) where k is a constant and t is the time in years. If the current population is 36,000, in how many years is the population expected to be 90,000? Round to the nearest year.
18 Years
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