Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Pattern Behaviors in Exponents

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #1 : How To Find Compound Interest

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Possible Answers:

$\$ 14,991.24$

$\$14,778.51$

$\$15,007.02$

$\$14,062.50$

$\$15,011.78$

Correct answer:

$\$ 14,991.24$

Explanation:

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and t = 5 , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Report an Error

Example Question #1 : Pattern Behaviors In Exponents

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Possible Answers:

$95 \%$

$85 \%$

$100 \%$

$90 \%$

$105 \%$

Correct answer:

$95 \%$

Explanation:

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

In the given scenario, t = 10 , r = 0.06735 , and N = 12 (monthly); substitute:

$A = A_{0}\left ( 1+ \frac{0.06735}{12} \right )^{12 \cdot 10}$

$A \approx A_{0}\left ( 1+0.0056125 \right )^{12 0}$

$A \approx A_{0}\left ( 1 .0056125 \right )^{12 0}$

$A \approx A_{0} \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Report an Error

Example Question #3 : How To Find Compound Interest

Donna wants to deposit money into a certificate of deposit so that in exactly ten years, her investment will be worth $100,000. The interest rate of the CD is 7.885%, compounded monthly.

What should Donna's initial investment be, at minimum?

Possible Answers:

$\$45,802.62$

More information is needed to answer the question.

$\$45,569.99$

$\$ 46,815.46$

$\$55,912.78$

Correct answer:

$\$45,569.99$

Explanation:

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

Set A = 100,000, r = 0.07885, N = 12 (monthly = 12 periods), and t = 10 , and evaluate $A_{0}$ :

$100,000 = A_{0} \left ( 1+ \frac{0.07885}{12} \right )^{12 \cdot 10}$

$100,000 \approx A_{0} \left ( 1+0.0065708\right )^{120}$

$100,000 \approx A_{0} \left ( 1 .0065708\right )^{120}$

$100,000 \approx A_{0} \cdot 2.1944$

$A_{0} \approx 100,000 \div 2.1944$

$A_{0} \approx 45,569.99$

The correct response is $45,569.99.

Report an Error

Example Question #1 : How To Find Compound Interest

Tom invests $\$15$ , 000 in a savings account with an annual interest rate of $6\%$ . If his investment is compounded semiannually, how much interest does he earn after years?

Possible Answers:

$\$1942.35$

$\$1841.31$

$\$1390.91$

$\$1758.45$

$\$1882.63$

Correct answer:

$\$1882.63$

Explanation:

In order to find the interest earned, used the compound interest formula

$\text{Final Balance} = \text{Principal} \cdot (1+\frac{IR}{C})^{(\text{Time})(\text{C})}$

where represents the number of times the account is compounded each year, and represents the interest rate expressed as a decimal.

$=15,000\cdot(1+\frac{.06}{2})^{(2)(2)}$

$=15,000\cdot(1+.03)^{4}$

$=15,000\cdot(1.03)^{4}$

=16882.63

The account is worth $16882.63 after two years. Therefore Tom earns $1882.63 in interest.

16882.63-15000=1882.63

Report an Error

Example Question #251 : Exponents

If a^x·a⁴ = a¹² and (b^y)³ = b¹⁵, what is the value of x - y?

Possible Answers:

-4

-2

-9

Correct answer:

Explanation:

Multiplying like bases means add the exponents, so x+4 = 12, or x = 8.

Raising a power to a power means multiply the exponents, so 3y = 15, or y = 5.

x - y = 8 - 5 = 3.

Report an Error

Example Question #1 : Pattern Behaviors In Exponents

If p and q are positive integrers and 27^p= 9^q, then what is the value of q in terms of p?

Possible Answers:

(2/3)p

(3/2)p

Correct answer:

(3/2)p

Explanation:

The first step is to express both sides of the equation with equal bases, in this case 3. The equation becomes 3^3p= 3^2q. So then 3p = 2q, and q = (3/2)p is our answer.

Report an Error

Example Question #1 : Pattern Behaviors In Exponents

Simplify 27^2/3.

Possible Answers:

125

729

Correct answer:

Explanation:

27^2/3 is 27 squared and cube-rooted. We want to pick the easier operation first. Here that is the cube root. To see that, try both operations.

27^2/3 = (27²)^1/3 = 729^1/3 OR

27^2/3 = (27^1/3)² = 3²

Obviously 3² is much easier. Either 3² or 729^1/3 will give us the correct answer of 9, but with 3² it is readily apparent.

Report an Error

Example Question #255 : Exponents

If and are integers and

$\left ( \frac{1}{3} \right )^{a}=27^{b}$

what is the value of $a\div b$ ?

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

To solve this problem, we will have to take the log of both sides to bring down our exponents. By doing this, we will get $\dpi{100} \small a\ast log\left (\frac{1}{3} \right )= b\ast log\left ( 27 \right )$ .

To solve for $\dpi{100} \small \frac{a}{b}$ we will have to divide both sides of our equation by $\dpi{100} \small log\frac{1}{3}$ to get $\dpi{100} \small \frac{a}{b}=\frac{log\left ( 27 \right )}{log\left ( \frac{1}{3} \right )}$ .

$\dpi{100} \small \frac{log\left ( 27 \right )}{log\left ( \frac{1}{3} \right )}$ will give you the answer of –3.

Report an Error

Example Question #256 : Exponents

If $\log 2=0.301$ and $\log 3=0.477$ , then what is $\log 12$ ?

Possible Answers:

1.079

1.116

1.592

1.346

1.255

Correct answer:

1.079

Explanation:

We use two properties of logarithms:

$log(xy) = log (x) + log (y)$

$log(x^{n}) = nlog (x)$

So $\log 12=2 \log2+\log3$

Report an Error

Example Question #1 : How To Find Patterns In Exponents

Evaluate:

$x^{-3}x^{6}$

Possible Answers:

$x^{3}$

$x^{-3}$

$x^{-18}$

$x^{6}$

$x^{9}$

Correct answer:

$x^{3}$

Explanation:

$x^{m}\ast x^{n} = x^{m + n}$ , here m=-3 and n=6 , hence -3+6=3 .

Report an Error

← Previous 1 2 3 Next →

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

View PSAT Mathematics Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View PSAT Mathematics Tutors

Nene
Certified Tutor

University of Science and Arts of Oklahoma, Bachelor of Science, Mathematics. Florida Institute of Technology, Master of Scie...

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Philadelphia, French Tutors in Atlanta, English Tutors in San Francisco-Bay Area, Chemistry Tutors in Houston, English Tutors in Houston, French Tutors in Phoenix, Physics Tutors in Seattle, SSAT Tutors in San Diego, Calculus Tutors in Seattle, Physics Tutors in Chicago

Popular Courses & Classes

SAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Houston, GRE Courses & Classes in Chicago, Spanish Courses & Classes in New York City, ACT Courses & Classes in Atlanta, ACT Courses & Classes in Denver, MCAT Courses & Classes in Seattle, ACT Courses & Classes in Philadelphia, GMAT Courses & Classes in Seattle, GRE Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Atlanta, ACT Test Prep in Philadelphia, LSAT Test Prep in San Diego, ACT Test Prep in Denver, LSAT Test Prep in Denver, ACT Test Prep in Atlanta, SSAT Test Prep in Houston, GRE Test Prep in New York City, GMAT Test Prep in Seattle

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

PSAT Math : Pattern Behaviors in Exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find Compound Interest

Example Question #1 : Pattern Behaviors In Exponents

Example Question #3 : How To Find Compound Interest

Example Question #1 : How To Find Compound Interest

Example Question #251 : Exponents

Example Question #1 : Pattern Behaviors In Exponents

Example Question #1 : Pattern Behaviors In Exponents

Example Question #255 : Exponents

Example Question #256 : Exponents

Example Question #1 : How To Find Patterns In Exponents

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: