Algebra 1B-Post Test: Exponential Relationships

Micah took out a student loan for $20,000, which began accruing interest immediately. He has chosen not to begin payment of the loan until he finishes his schooling. The table shows the balance of the loan while Micah is in school. Months Loan Balance 6 $20,608 12 $21,234 18 $21,879 24 $22,543 30 $23,228 36 $23,934 Assuming that the relationship is exponential, which is the best estimate of the loan balance after 4 years?

$25,410

The table below represents an exponential function, g, that has been vertically shifted from the parent function, f(x) = 2x. x 0 1 2 3 4 g(x) -11 -10 -8 -4 4 Determine the size of the shift from function f to function g. Then, plot the points of a function that is shifted only half as much as g from the parent function, f. Use the same x-values as used in the table for function g.

(0, -5) (1, -4) (2, -2) (3, 2) (4, 10)

What is the domain of the function shown on the graph?

-∞ < x < ∞

What is the range of the function graphed below?

-∞ < y < 2

Peter is conducting a chemical experiment in a controlled environment. The initial temperature of the chemical solution was 20°C. The temperature of the solution was 1.5 times the initial temperature after 3 minutes. The temperature of the solution continued to increase at this rate. This situation is graphed below. Let x represent the number of minutes passed after the start of the experiment, and let f(x) represent the temperature of the solution. Once the temperature reached 45°C, the experiment was stopped. Over which interval did Peter conduct the experiment?

0 ≤ x ≤ 6

A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 · b^n, where n is the number of hours and b is an unknown positive base. Based on the model, there were initially __________ bacteria. If b = 1.85, the hourly percent growth rate of the bacteria would be ___________%

20 85%

Jim is assessing the popularity of his high school football team's website for the first 5 weeks after the season ends. The average number of visits on the website for 5 weeks is given in the table below. Number of Weeks Avg. Number of Visits 0 48,000 1 24,000 2 12,000 3 6,000 4 3,000 5 1,500 The percent decrease in the average number of visits each week since the end of the season was _______________%

50

Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. g(x) = 18(1/3)^x + 2 Which statement correctly compares the two functions on the interval [-1, 2]?

Both functions are increasing, but function g increases at a faster average rate.

Exponential function f is represented by the table. x -1 0 1 2 3 f(x) 78 24 6 0 -2 Function g is an exponential function passing through the points (0,15) and (2,0). Which statement correctly compares the behavior of the two functions on the interval (0, 2)?

Both functions are positive and decreasing on the interval.

There were 800 farmers' markets initially in the USA in 2012. In 2013, the number of farmers' markets was 1.25 times the initial number of farmers' markets. Then, in 2014, the number of farmers' markets was 1.25 times the number of farmers' markets the previous year. If this pattern continues, which of the following graphs represents the number of farmers' markets in the USA over time?

Graph Z points (0, 800) and (1, 1,000)

The Sawyer and Ruiz families each bought a laptop computer at the same time. The resale values, in dollars, of the laptops are modeled by the given functions, where x is the number of years that each family has owned the laptop. Sawyer Family's Laptop f(x) = 620(0.85)^x Ruiz Family's Laptop x g(x) 0 640 2 480 4 360 The ______________ family's laptop has the greater initial resale value. During the first four years, the resale value of the Sawyer family's laptop decreases at an average rate ___________________ the resale value of the Ruiz family's laptop.

Ruiz faster than

Consider the function f(x) = 10^x and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of f(x)? g(x) = f(x -6) = 10^(x -6)

The graph of g(x) is the graph of f(x) shifted to the right 6 units.

Consider the function f(x) = 2x and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)? g(x) = 2f(x) = 2(2^x)

The graph of g(x) is the graph of f(x) stretched vertically by a factor of 2.

The graph of function f is shown Function g is represented by the equation. g(x) = 4(1/4)^x + 2 Which statement correctly compares the two functions?

They have different y-intercepts but the same end behavior.

The graph of function f is shown. Function g is represented by the table. x -1 0 1 2 3 g(x) 15 3 0 Which statement correctly compares the two functions?

They have the same x-intercept but different end behavior as x approaches ∞.

Consider the function shown below. g(x) = 2^x If the function g is horizontally compressed by a factor of 1/2 and reflected across the x-axis to obtain function f, which of the following graphs matches the above transformation?

Y points (0, -1) and (-2, 0) (-3, 0) (-4, 0)

Paul uploaded a video of skateboarding tricks on a popular social media platform. Initially, only 5 of his close friends viewed his video. The number of views that he received doubled every day. Which of the following graphs represents the number of views at the end of each day?

Z (0, 5) (1, 10)

What are the asymptote and the y-intercept of the function shown in the graph? f(x) = 3(0.2)^x + 2

asymptote: y = 2 y-intercept: (0,5)

Micah took out a student loan for $20,000, which began accruing interest immediately. He has chosen not to begin payment of the loan until he finishes his schooling. The table shows the balance of the loan while Micah is in school. Months Loan Balance 6 $20,608 12 $21,234 18 $21,879 24 $22,543 30 $23,228 36 $23,934 Assuming that the relationship is exponential, which equation best represents the curve of best fit for this set of data?

f(x) = 20,000 • 1.005^x

Which equation best represents the curve of best fit for this data?

f(x) = 51.5 • 0.92^x

The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g? Replace the values of h and k in the equation.

g(x) = 2^ (x + 7) + -1

The value of a car depreciates every two years. The value of the car after t years is shown by the following expression. 25,250(0.87)^t/2 Which best describes the coefficient, 25,250?

the initial value of the car

On the provided graph, plot the points where the following function crosses the x-axis and the y-axis. g(x) = -5^x + 5

x- axis (1, 0) y-axis (0, 4)

Due to an increasing population, developed land in a region is increasing at a rate of 12% per year. If there are currently 8,500 square miles of developed land, which equation models the square mileage of developed land, y, after x years?

y = 8,500(1.12)^x

Which graph represents the given exponential function? f(x) = 5(3)^x - 1

y- axis (0, 4) x- axis (0, between -1 and 2)