Chapter 4 Math Quiz

Water hyacinth is an invasive plant species found in many lakes that typically grows at a rate of 7% per day. As part of a study, a scientist introduces a 150-gram sample of water hyacinth into a testing pool. Which of the following functions gives the amount of water hyacinth in the testing pool weeks after the sample is introduced? (Note: 1 week is 7 days.)

k(t)=150(1.07^(7))^t

The logarithmic function f is defined by f(x) = log3(x) on a domain of f is 0 < x ≤ 9. Which of the following is true of f?

f has a maximum value, but no minimum value.

The function f is given by f(x) = 2log5(x). Which of the following describes f?

f is an increasing function that increases at a decreasing rate.

The range of function f is the positive real numbers. The function g is given by g(x) = ln(f(x)). Solutions to which of the following equations are useful in solving g(x) = 2?

f(x) = e^2

The functions f and g are given by f(x)= 4(5x-1) and g(x)= 8(x-4) . When solving the equation f(x)=g(x) the functions can be rewritten in equivalent forms so that the equation can be solved without the use of technology. Which of the following are equivalent definitions of f and g that aid in solving f(x)=g(x) without the use of technology?

f(x)=2^(log2(5x-1) and g(x)=2^(log2 8(x/4)

x: 1, 2, 3, 4 f(x): 2, 4, 8, 16 The table gives values of the function f for selected values of x. Which of the following is a verbal representation of f^-1 (x), the inverse function of f?

f^-1 (x) is logarithmic with output values increasing by every time input values double.

Which of the following is the inverse of the function f given by f(x) = 4log2(x + 3) - 1?

g(x) = 2(x+1/4) -3

The initial population size of an animal species is measured to be 2000. The population doubles every 8 years. Which of the following functions gives the time, in years, as an output value, and a certain number x for the population size as an input value?

h(x) = 8log2(x/2000)

Which of the following could describe a single logarithmic function f?

lim f(x): x->0+ = ∞ and lim f(x): x-> ∞ = -∞

The function g is given by g(x) = a log b (c), where a, b, and c are positive integers. Which of the following is an equivalent representation of g(x)?

log b (c^a)

The function g is given by g(x) = log7(x), and the function h is given by h(x) = log49(x). Which of the following describes the relationships between g and h?

For equal input values, the output values of h are half the output values of g.

The function f is given by f(x) = ln x. Which of the following describes input values for which the output values of f are integers?

Integer powers of e

A decibel (dB) is a unit of measure for loudness of sound. The decibel scale is based in sound intensity N, in watts per square meter. A decibel value is given by the function d, where d(N) = 10log10(N/10^-12). Which of the following gives all intensities N, in watts per square meter, for which the decibel value is greater than 140 decibels?

N > 100

The value (2x2x2x2x2x4.7) is the output value of an exponential function of the form f(x)= axb^x, where a and b are constants. Which of the following describes the function and input value that corresponds to this output value?

The exponential function has an initial value of 4.7 and a base of 2 and the input value is 5.

The function f is given by f(x)= 5x(0.7)^x. Which of the following describes f?

The function f model exponential decary and lim x --->∞ f(x)=0.

The function f is given by f(x)=3^x . The function g is given by g(x)=f(x))^b, where b is less than 0. Which of the following describes the relationship between the graphs of f and g?

The graph of g is a combination of a horizontal dilatation of the graph of f and a reflection over the y-axis.

The functions f and g are given by f(x)=2^x and g(x)=2^x and g(x)=2^x2^a, where a is greater than 0 . Which of the following describes the relationship between the graph of f and the graph of g?

The graph of g is a horizontal translation of the graph of f by -a units.

The function g is a function of the form g(x)= axb^x, where a is not equal to 0 and b is greater than 0. The function f is given by f(x)=g(x)+4. Which of the following statements is true?

The output values of g only, not f, are proportional over equal-length input value intervals.

Iodine-131 has a half-life of 8 days. In a particular sample, the amount of iodine-131 remaining after d days can be modeled by the function h given by h(d) = A0(0.5)^(d/8), where A0 is the amount of iodine-131 in the sample at time d= 0. Which of the following functions models the amount of iodine-131 remaining after t hours, where A0 is the amount of iodine-131 in the sample at time t = 0? (There are 24 hours in a day, so t = 24d .)

k(t) = A0(0.5 ^(1/192) )^t

Let k, w, and z be positive constants. Which of the following is equivalent to kz/w^2?

log10k + log10z - 2log10w

The function f is given by f(x) = log2(x). Which of the following is equivalent to f(7)?

log3(7) / log3(2)

The function h is given by h(x) = log3(x) . Which of the following is equivalent to the expression 2 • h(w) + h(p), where w and p are values in the domain of h?

log3(w^2 p)

The function f is an increasing function such that every time the output values of the function f increase by 1, the corresponding input values multiply by 4. Which of the following could define f(x)?

log4x

The exponential function g is given by g(x)=5^x. Which of the following expressions defines g^-1(x)?

log5x

The function g is given by g(x) = ln(3x = 1) - ln(x^2 + x - 2). What are all values of x for which g(x) < 0?

(3, ∞) only

The sales of a new product, in items per month, is modeled by the expression 225 + 500log10(15t + 10), where t represents the time since the product became available for purchase, in months. What is the number of items sold per month for time t = 6?

1225

An equation involves the expression log9(27^x) , which is equivalent to a rational multiple of x. By rewriting the expression in an equivalent form, the value of the rational number can be determined without use of a calculator or complicated calculations. Which of the following is an equivalent expression that satisfies this requirement?

(x ln 27)/(ln 9)

The function f is logarithmic, and the points (2,1) and (4,2) are on the graph of f in the xy-plane. Which of the following could define f(x)?

2log4(x)

x: 0, 2, 4, 6 f(x): 3, 48, 768, 12,288 The table gives values of the function f for selected values of x. Which of the following expressions could define f(x)?

3 • 4^x

The function f is given by f(x)=log2(log3x). Which of the following is an expression for f^-1(x)?

3^(2x)

The function k is given by k(x)=9^x . Which of the following expressions also defines k(x) ?

3^(2x)

If m = log3(81), which of the following is also true?

3^m = 81

The function h is given by h(x)= 5x3^(-x/2). What is the value of h(1)?

5/√3

The value, in millions of dollars, of transactions processed by an online payment platform is modeled by the function M . The value is expected to increase by 6.1% each quarter of a year. At time t=0 years, 54 million dollars of transactions were processed. If t is measured in years, which of the following is an expression for ? (Note: A quarter is one fourth of a year.)

54(1.061)^(4t)

The function m is given by m(x)= 36^(x/2). Which of the following expressions could also define m(x)?

6^x

The function f is given by f(x)=2^x and the function g is given by g(x)= f(x)/8. For which of the following transformations is the graph of g the image of the graph of f?

A horizontal translation to the right 3 units.

The function f is given by f(x) = log10(x). The function g is given by g(x) = log10(x)^3. Which of the following describes a transformation for which the graph of is the image of the graph of f?

A vertical dilation by a factor of 3

In a certain town, the population in the year 2000 was about 30,000. The population grows at a rate of 2.3% per year, and time is measured in years since 2000. Which of the following functions gives output values, in years since 2000, for input values of the town's population p?

g(p) = log1.023(p/30,000)

What are all values of x for which ln(x^3) - ln x = 4?

x = e^2 only

To solve the equation log8(x - 3) + log8(x +4) = 1, one method is to apply the properties of logarithms to rewrite the equation in an equivalent form. This equivalent equation can be used to identify possible solutions. Of the following, which is such an equation?

x^2 = x - 12 = 8