Order the group of quadratic functions from widest to narrowest graph.
yequals3xsquared, yequalsnegative one fourth
xsquared, yequalsnegative two fifths
xsquared
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Part 1
Choose the correct answer below.
A.
yequalsnegative one fourth
xsquared, yequals3xsquared, yequalsnegative two fifths
xsquared
B.
yequals3xsquared, yequalsnegative one fourth
xsquared, yequalsnegative two fifths
xsquared
C.
yequalsnegative two fifths
xsquared, yequals3xsquared, yequalsnegative one fourth
xsquared
D.
yequalsnegative one fourth
xsquared, yequalsnegative two fifths
xsquared, yequals3xsquared
E.
yequals3xsquared, yequalsnegative two fifths
xsquared, yequalsnegative one fourth
xsquared
F.
yequalsnegative two fifths
xsquared, yequalsnegative one fourth
xsquared, yequals3xsquared
F. y = -2/5x^2, y = -1/4x^2, y = 3x^2
Find the number of real-number solutions of the equation below.
x squared minus 4 x plus 5 equals 0
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Part 1
Choose the correct answer below.
A.
The equation has one real-number solution.
B.
The equation has two real-number solutions.
C.
The equation has no real-number solution.
C. The equation has no real-number solution.
Which type of function best models the set of data points?
left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 5 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 3 comma 7 right parenthesis, (4,14)
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Part 1
Which of the following functions is the most appropriate?
Linear model
Quadratic model
None
Exponential model
A linear model is the most appropriate for the set of data points provided.
Which type of function best models the data set?
(negative 1,8), (0,6), (2,3.84), (3,2.88)
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Part 1
Choose the correct answer below.
None
Quadratic model
Linear model
Exponential model
A quadratic model is the most appropriate for the set of data points provided.
Determine whether the following table represents an exponential function. Explain why or why not.
x
0
1
2
3
y
6
9
27
33
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Part 1
Does the table represent an exponential function? Why or why not?
A.
Yes, all of the x-values have a constant difference, and all of the y-values have a constant ratio.
B.
Yes, all of the x-values have a constant ratio, and all of the y-values have a constant difference.
C.
No, all of the x-values have a constant ratio, but all of the y-values do not have a constant difference.
D.
No, all of the x-values have a constant difference, but all of the y-values do not have a constant ratio.
D. No, all of the x-values have a constant difference, but all of the y-values do not have a constant ratio.
In an exponential function, the y-values would have a constant ratio as x increases. Here, the y-values do not exhibit a consistent exponential growth pattern, so it is not an exponential function.
Suppose that when your friend was born, your friend's parents deposited $5000 in an account paying 6.9% interest compounded quarterly. What will the account balance be after 13 years?
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Part 1
The balance after 13 years will be $
enter your response here.
(Round to the nearest cent as needed.)
To calculate the balance after 13 years with quarterly compounding, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial principal (initial deposit in this case)
r = annual interest rate (6.9% or 0.069)
n = number of times interest is compound per year (quarterly compounding, so n = 4)
t = number of years (13 years)
Plugging in the values, we get:
A = $5000(1 + 0.069/4)^(4*13)
A = $5000(1 + 0.01725)^52
A = $5000(1.01725)^52
A ≈ $12296.46
Therefore, the account balance will be approximately $12,296.46 after 13 years.