The table shows the number of shoppers at Jacob's store over a period of five months:
Month 1 2 3 4 5
Shoppers 50 250 1,250 6,250 31,250
Did the number of people at Jacob's store increase linearly or exponentially?
Linearly, because the table shows an equal increase in number of shoppers for an equal increase in months
Exponentially, because the table shows an equal increase in number of shoppers for an equal increase in months
Linearly, because the table shows the number of shoppers increases by an equal factor for an equal increase in months
Exponentially, because the table shows the number of shoppers increases by an equal factor for an equal increase in months
Exponentially, because the table shows the number of shoppers increases by an equal factor for an equal increase in months
What is 3 to the power of two thirds equal to?
cube root of 9
square root of 9
cube root of 27
square root of 27
Cube root of 27
Which graph best represents the function f(x) = 4(1.5)x?
graph of increasing exponential function going through point 0, 2
graph of increasing exponential function going through point 0, 3
graph of increasing exponential function going through point 0, 1
graph of increasing exponential function going through point 0, 4
The graph of increasing exponential function going through point 0, 1 best represents the function f(x) = 4(1.5)^x.
Simplify square root of 2 over cube root of 2
To simplify the expression square root of 2 over cube root of 2, we can rewrite it as (2^(1/2))/(2^(1/3)).
Using the property of exponents, we can simplify this to 2^[(1/2)-(1/3)].
Next, we will find a common denominator for 2/3 and 1/2, which is 6.
So, we get 2^[(3/6)-(2/6)] = 2^(1/6).
Therefore, the simplified form of square root of 2 over cube root of 2 is 2^(1/6).
A function is shown:
f(x) = (1.93)x
What does the function represent?
Exponential growth of 7%
Exponential decay of 7%
Exponential growth of 93%
Exponential decay of 93%
The function f(x) = (1.93)x represents exponential growth of 93%.
The functions f(x) and g(x) are described using the following equation and table:
f(x) = −6(1.02)x
x g(x)
−1 −5
0 −3
1 −1
2 1
Which equation best compares the y-intercepts of f(x) and g(x)?
The y-intercept of f(x) is equal to the y-intercept of g(x).
The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).
The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).
The y-intercept is the value of the function when x is equal to zero.
For f(x) = -6(1.02)^x, when x is equal to 0, we have f(0) = -6(1.02)^0 = -6(1) = -6.
Therefore, the y-intercept for f(x) is -6.
For g(x), we can see from the table that when x is equal to 0, g(0) = -3.
Therefore, the y-intercept for g(x) is -3.
From the given options, the equation that best compares the y-intercepts of f(x) and g(x) is:
The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
A survey was conducted among 400 students in groups ages 7–12 and 13–18 to find their favorite music genre. The students had to select any one genre from jazz, rock, or pop. Out of the 200 students in the age group 7–12 who participated in the survey, 142 liked rock or pop music. The total number of students of both age groups who liked jazz was 72.
Using a two-way table, compute the total number of students in the age group 13–18 who liked rock or pop music.
122
130
142
186
To compute the total number of students in the age group 13–18 who liked rock or pop music, we can use the information provided in the two-way table.
Let's label the categories of the table:
| Jazz | Rock/Pop | Total
-----------------------------------------
Age group 7–12 | 72 | 142 | 200
-----------------------------------------
Age group 13–18 | ? | ? | ?
We know that the total number of students in the age group 7–12 who liked rock or pop music is 142. The total number of students in this age group is given as 200.
Now, let's calculate the total number of students in the age group 13–18 who liked rock or pop music.
To do this, we can subtract the number of students in the age group 7–12 who liked rock or pop music from the total number of students who participated in the survey:
Total number of students in the age group 13–18 who liked rock or pop music = Total number of students - Number of students in the age group 7–12 who liked rock or pop music
= 400 - 200
= 200.
Therefore, the total number of students in the age group 13–18 who liked rock or pop music is 200.
Answer: 200
A survey was conducted among 400 students in groups ages 7–12 and 13–18 to find their favorite music genre. The students had to select any one genre from jazz, rock, or pop. Out of the 200 students in the age group 7–12 who participated in the survey, 142 liked rock or pop music. The total number of students of both age groups who liked jazz was 72.
Using a two-way table, compute the total number of students in the age group 13–18 who liked rock or pop music.
a. 122
b. 130
c. 142
d. 186
To compute the total number of students in the age group 13–18 who liked rock or pop music, we can use the information provided in the two-way table.
Let's label the categories of the table:
| Jazz | Rock/Pop | Total
-----------------------------------------
Age group 7–12 | 72 | 142 | 200
-----------------------------------------
Age group 13–18 | ? | ? | ?
We are given that the total number of students who participated in the survey is 400, and the total number of students in the age group 7–12 who liked rock or pop music is 142.
To find the total number of students in the age group 13–18 who liked rock or pop music, we need to subtract the number of students in the age group 7–12 who liked rock or pop music from the total number of students who participated in the survey.
Total number of students in the age group 13–18 who liked rock or pop music = Total number of students - Number of students in the age group 7–12 who liked rock or pop music
= 400 - 142
= 258
Therefore, the total number of students in the age group 13–18 who liked rock or pop music is 258.
Answer: The correct option is d. 258 students.
Home values are expected to increase by 5% per year. Hadlee recently purchased a home for $240,000. Which of the following equations can be used to represent the value of the home x years after the purchase?
f(x) = 5(0.95)x
f(x) = 5(1.05)x
f(x) = 240000(0.95)x
f(x) = 240000(1.05)x
The value of the home is expected to increase by 5% per year, which means it will be multiplied by a factor of 1.05 each year.
Since Hadlee purchased the home for $240,000, the equation to represent the value of the home x years after the purchase would be:
f(x) = 240000(1.05)x.
Thus, the correct equation is f(x) = 240000(1.05)x.