Post Test: Exponential and Logarithmic Functions

Consider the graph of the function f(x)=e^x. What is the range of function g if g(x)=f(x)+3?

A. (3, infinity)

The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, I0. m=log(I / I zero) Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?

A. M=log(10,000)

Which graph represents this exponential function? f(x)=3⁢(2)x−4

B.

Select the correct answer. What is the approximate sum of this series? ∑k=1,8 terms 5⁢(4/3)(k−1)

B. 134.83

Seth is trying to pay off his credit card. He plans to pay it off in 24 months. Interest on the card is compounded monthly at a fixed annual rate of 11.6%. Seth currently has a balance of $18,875 on his credit card. Use the formula for the sum of a finite geometric series to determine Seth's approximate monthly payment.

Seth's approximate monthly payment will be $884.99.

Bacteria begins to grow on the water's surface in a non-operational swimming pool on September 20. The bacteria grows and covers the water's surface in such a way that the area covered with bacteria doubles every day. If it continues to grow in this way, the water's surface will be entirely covered with bacteria on September 28. When will a quarter of the water's surface be covered?

The water's surface will be covered a quarter of the way on September 26.

Consider the graph of the function f(x)=(14)^x. Which statements describe key features of function f?

y-intercept at (0,1) range of 0<y<+infinity horizontal asymptote of y=0

Select all the correct answers. Consider the graph of the function f(x)=log BASE 2 of x. What are the features of function g if g(x)=f(x+4)+8?

y-intercept at (0,10) vertical asymptote of x = -4

In 2016, 5,200 parking permits were issued in a city. The number of parking permits increases by 5% every year. Let y represent the number of parking permits issued x years since 2016. Which type of sequence does the situation represent?

The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Consider function f and function g. f(x)=ln⁡x g(x)=-5⁢ln⁡x How does the graph of function g compare with the graph of function f?

Unlike the graph of function f, the graph of function g decreases as x increases. The graphs of both functions have a vertical asymptote of x=0. The graph of function g is the graph of function f vertically stretched by a factor of 5.

Select the correct answer from each drop-down menu. Maite has money in an interest-bearing account. The table shows how much money is in the account at the end of each year. YearAmount 1--$1,000.00 2--$1,030.00. 3--$1,060.90 4--$1,092.73 5--$1,125.51

a geometric ratio 1.03 NOT: 1159.28 (that was wrong)

Select the correct answer. Which function has an asymptote at x = 5 and an x-intercept of (6,0)?

f(x) = log(x − 5)

Consider the graph of the function f(x)=2^x. Which statements describe key features of function g if g(x) = f(x+2)?

horizontal asymptote of y=0 y-intercept at (0,4) domain of -infinity < x, < + infinity

The sales of vinyl records have increased due to a revived popularity. In the year 2012, 50,000 records were sold. Every following year, the number of records sold were 1.1 times the number of records sold the previous year. How many vinyl records were sold in 2016?

D. 73205

Consider the graph of the function f(x)=10^x. What is the y-intercept of function g if g(x)=-4⁢f(x)+12?

(0,8)

Select the correct answer. What is the y-intercept of f(x) = 3x+2?

(0,9)

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares. Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.

1023

Select the correct answer. What is the sum of the first eight terms in this series? 2+10+50+250+⋅⋅⋅

195,312

Type the correct answer in the box. Use numerals instead of words. The graphs of functions f and g are shown. Function g is defined as g(x)=k * f(x). What is the value of k? The value of k is .

2

Select ALL the correct answers. Martha works at a small jewelry store. She designs 2 rings in the first hour. Every additional hour, she designs 3 new rings. Select all the functions that can be used to find the number of rings, r(n), she designs in n hours.

r(1)=2; r(n) = r(n-1) + 3, for n>=2 r(n) = 3n -1