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Units 7-8 Review

Last updated almost 4 years ago
31 questions
Note from the author:
Formula Sheet

If you don't have a TI calc at home, you may need these:
Linear Regression
Quadratic Regression
Exponential Regression
Formula Sheet

If you don't have a TI calc at home, you may need these:
Linear Regression
Quadratic Regression
Exponential Regression
1

Let A be a positive real number. Which is always true as x\rightarrow\infty?

1

Find the value of x that satisfies the equation.

2^{x} = 21

Enter your answer as a number rounded to 2 decimal places.

1

Find the value of x that satisfies the equation.

21^{x+5} = 2

Enter your answer as a number rounded to 2 decimal places.

1

Find the value of x that satisfies the equation.

21-3^{x+5} = 2

Enter your answer as a number rounded to 2 decimal places.

1

Find the value of x that satisfies the equation.

21+e^{2x+5} = 42

Enter your answer as a number rounded to 2 decimal places.

1

Find the value of x that satisfies the equation.

2\cdot 4^{3x-7}-18 = 42

Enter your answer as a number rounded to 2 decimal places.

1
Consider f(x) = 2 \cdot (\frac{2}{3})^{x}-5

f(x) is exponential _______ . (Type "growth" or "decay", no spaces or ")
f(x) has an asymptote of _______ . (Your answer should include a "=", no spaces, ex. z=5)
As x -> \infty, f(x) -> _______ . (Type a number, \infty, or -\infty).
As x -> -\infty, f(x) ->_______ . (Type a number, \infty, or -\infty).

For \infty, use copy paste from this question.
1
Consider f(x) = \frac{4}{3} \cdot (\frac{5}{4})^{x}

f(x) is exponential _______ . (Type "growth" or "decay", no spaces or ")
f(x) has an asymptote of _______ . (Your answer should include a "=", no spaces, ex. z=5)
As x -> \infty, f(x) -> _______ . (Type a number, \infty, or -\infty).
As x -> -\infty, f(x) ->_______ . (Type a number, \infty, or -\infty).

For \infty, use copy paste from this question.
1
Consider f(x) = ln(x+7)+3

f(x) has an asymptote of _______ . (Your answer should include a "=", no spaces, ex. z=5)
As x -> \infty, f(x) -> _______ . (Type a number, \infty, or -\infty).

For \infty, use copy paste from this question.
1
Consider f(x) = log_{\frac{1}{2}}(x)-2

f(x) has an asymptote of _______ . (Your answer should include a "=", no spaces, ex. z=5)
As x -> \infty, f(x) -> _______ . (Type a number, \infty, or -\infty).

For \infty, use copy paste from this question.
Devin opens a savings account with an initial deposit of 5000. He earns 8% annual interest.
1

Write an equation to find the value of the account after t years.

Use "y=..." format, no spaces.

1

Write an equation to find the value of the account after t months.

Round your base to five decimal places.

Use "y=..." format, no spaces.

1

How much more money would Devin earn if he got 8% interest compounded monthly for 5 years, rather than 8% annually for 5 years?

Enter your answer as a number rounded to two decimal places.

Rodric bought his car for 13000 in 2010. Since 2010, the car's value has depreciated by 10% annually.
1

Write an equation to find the value of the car after t years since 2010.

Use "y=..." format, no spaces.

1

Write an equation to find the value of the car after t months since 2010.

Round your base to five decimal places.

Use "y=..." format, no spaces.

1

Regression is run for a data set, and the r-values are given below.

LinReg: 0.9108
QuadReg: 0.9918
ExpReg: 0.9981
LnReg: 0.9206

Which model best fits the data?

Run QuadReg to create a function for the data below. Round your coefficients to three decimal places.

1

Predict the value of y when x=15.

Enter your answer as a number rounded to 2 decimal places.

Run ExpReg to create a function for the data below. Round your coefficients to three decimal places.
1

Predict the value of y when x=15.

Enter your answer as a number rounded to two decimal places.

1

Predict the value of x when y=10.

Enter your answer as a number rounded to two decimal places.

1
A data set has a mean of 100 and a standard deviation of 15.

The z-score for a data value of 112 is _______ .
The z-score for a data value of 80 is _______ .

For a z-score of 1.31, _______ % of the population is greater than that data value.
For a z-score of 1.31, _______ % of the population is less than that data value.

For all blanks, enter a number rounded to two decimal places.
1
A data set has a mean of 75 and a standard deviation of 8.2.

The z-score for a data value of 70 is _______ .
The z-score for a data value of 90 is _______ .

For a z-score of -0.88, _______ % of the population is greater than that data value.
For a z-score of -0.88, _______ % of the population is less than that data value.

For all blanks, enter a number rounded to two decimal places.
100 college students were surveyed about their major and their ACT score - whether they scored higher in math/science than English/reading or vice versa. The results are shown in the table below.
1

If a student is randomly selected from the group, what is the probability, as a percent, that they are an engineering major?

Enter your answer as a number rounded to two decimals, no spaces or "%".

1

If a student is randomly selected from the group, what is the probability, as a percent, that they are an engineering major or had a high STEM score?

Enter your answer as a number rounded to two decimals, no spaces or "%".

1

If a student is randomly selected from the group, what is the probability, as a percent, that they are an engineering major and had a high STEM score?

Enter your answer as a number rounded to two decimals, no spaces or "%".

1

If a student is randomly selected from the group, what is the probability, as a percent, that they are an engineering major given that they had a high STEM score?

Enter your answer as a number rounded to two decimals, no spaces or "%".

1

Are major and ACT strength dependent or independent events?

A furniture store contains lots of pillows. Some are blue, some are not, and some are square, some are round. The numbers of each are represented by letters in the following table.


Probabilities may be expressed by doing arithmetic with the letters. For example, P(square) = #square/total = \frac{A+B}{A+B+C+D}.
1

What is P(Round)?

Use the format given in the problem.

1

What is P(Round and Blue)?

Use the format given in the problem.

1

What is P(Round | Blue)?

Use the format given in the problem.

1

What is P(Blue | Square)?

Use the format given in the problem.

1

What is P(Blue or Square)?

Use the format given in the problem.