EOC Review Part III

Exponential function f(x) has a y-intercept of 3 and an x-intercept of -2. The function is always increasing as the values of x increase, but the function never reaches y = 4.

Which graph represents the information stated?

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Marcus buys $1,000 worth of stock in a company. He expects the value of the stock to increase by 5% each year.

Which equation could Marcus use to predict the stock's value x years after he purchases the stock?

• f(x) = 1,000(5)^x

• f(x) = 1,000(x)⁵

• f(x) = 1,000(1.05)^x

• f(x) = 1,000(x)^1.05

The first five terms of a pattern are shown.

9, 27, 81, 243, 729

The equation S_n = a(b)ⁿ can be used to calculate the value, S_n, of any term, n, in the pattern. What are the values of a and b in the equation?

• a = 1, b = 3

• a = 3, b = 3

• a = 3, b = 9

• a = 9, b = 9

A scientist studied the relationship between the number of trees, x, per acre and the number of birds, y, per acre in a neighborhood. She modeled the relationship with a scatter plot and used the equation y = 4 + 6x for the regression line.

What is the meaning of the slope and y-intercept of this regression line?

• The slope is 6. This means that the average number of birds per acre in an area with no trees is 6. The y-intercept is 4. This means that for every 1 additional tree, she can expect an average of 4 additional birds per acre.

• The slope is 4. This means that for every 1 additional tree, she can expect an average of 4 additional birds per acre. The y-intercept is 6. This means that the average number of birds per acre in an area with no trees is 6.

• The slope is 6. This means that for every 1 additional tree, she can expect an average of 6 additional birds per acre. The y-intercept is 4. This means that the average number of birds per acre in an area with no trees is 4.

• The slope is 4. This means that the average number of birds per acre in an area with no trees is 4. The y-intercept is 6. This means that for every 1 additional tree, she can expect an average of 6 additional birds per acre.

Kendra and Theo each collected data on the number of birds they observed at a bird feeder each hour for eight hours. The range of Kendra's data is 6. The median of Kendra's data is 7. The mean of Kendra's data is 7.

The data Theo collected have the same range and the same median as the data Kendra collected, but the mean of Theo's data is 7.5. The line plot correctly shows six of the eight data points for Theo's data set. Where should be remaining two data points be on the line plot?

• There should be a data point at 5 and 6.

• There should be a data point at 9 and 11.

• There should be a data point at 7 and 12.

• There should be a data point at 5 and 12.

Which set of data points could BEST be modeled by a line of best fit that is a decreasing linear function?

• {(0, 0), (1, 8), (2, 15), (3, 22), (4, 30)}

• {(0, 5), (1, 6), (2, 10), (3, 16), (4, 28)}

• {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}

• {(0, 64), (1, 60), (2, 52), (3, 39), (4, 22)}

Which set of data could be BEST modeled by a quadratic function?

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The number of customers that visited a store certain number of hours after the store opened at 8 a.m. are shown in the table.

After plotting the points, which statement BEST describes the data?

• The data can be modeled by a linear function.

• The data can be modeled by a constant function.

• The data can be modeled by a quadratic function.

• The data can be modeled by an exponential function.

Triangle ABC has vertices as shown.

• 12 square units

• 24 square units