Question

Two scientists are running experiments on the same type of bacteria in different control groups. The results are shown in the graph using the functions f(x) and g(x): graph of two functions with quadrant 1 and 4 shown, f of x equals seven times one half to the x power plus three and g of x equals one half times x minus one Which statement best describes the graph of f(x) and g(x)? The graph of f(x) will eventually exceed the graph of g(x). The graph of g(x) will eventually exceed the graph of f(x). The graphs will both have their y-intercept equal to −1. The graphs will both have their y-intercept equal to 8. Question 4(Multiple Choice Worth 1 points) (03.05 MC) Bob opened a new furniture store, and his daily sales are modeled by f(x) = 1000(1.15)x. Determine the rate of growth. 1000% 115% 15% 85% Question 5(Multiple Choice Worth 1 points) (03.05 MC) The amount of a radioactive material changes with time. The table below shows the amount of radioactive material f(t) left after time t: t(hours) 0 1 2 f(t) 100 50 25 Which exponential function best represents the relationship between f(t) and t? f(t) = 0.5(100)t f(t) = 100(0.25)t f(t) = 0.25(50)t f(t) = 100(0.5)t Question 6(Multiple Choice Worth 1 points) (03.05 MC) Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio? The common ratio is 0.99. The common ratio is 1.05. The common difference is 0.42. The common difference is 0.84. Question 7(Multiple Choice Worth 1 points) (03.05 LC) Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation? f(x) represents the total number of hours; x represents the number of weeks he exercises this summer. f(x) represents the total number of weeks

Answer 1

The graph shows that the population of bacteria in the experiment represented by g(x) will eventually exceed the population of bacteria in the experiment represented by f(x). Therefore, the correct option is 2. The graph of g(x) will eventually exceed the graph of f(x).

The graph shows the results of two experiments on the same type of bacteria, with the results plotted as functions of time. The function f(x) is represented by the blue line, and the function g(x) is represented by the green line.

Analyze f(x)

f(x) starts at positive infinity on the y-axis. This means that the bacteria in the experiment represented by f(x) initially have a very large population.

The line f(x) then decreases rapidly as x increases. This means that the population of bacteria in the experiment represented by f(x) is decreasing rapidly over time.

Analyze g(x)

g(x) starts at a lower y-value than f(x) and increases as x increases. This means that the population of bacteria in the experiment represented by g(x) is smaller than the population in the experiment represented by f(x) at the beginning of the experiment, and it is also increasing over time.

The lines f(x) and g(x) intersect at a point where x is approximately 2. This means that at this time point, the populations of bacteria in the two experiments are equal.

After the point of intersection, the line g(x) continues to increase, while the line f(x) continues to decrease. This means that the population of bacteria in the experiment represented by g(x) is eventually greater than the population in the experiment represented by f(x).

Option 2 is the right choice.