Which Expressions are Equivalent to 3^4 • 3^x?

Which expressions are equivalent to 3^4 • 3^x ? There is more than one way to skin a cat...okay gross analogy but it is just a saying...and I'm just sayin'. 

Let's use the MathPapa calculator to figure it out.

Plug in your options. You want to know if one formula equals another, so put the one in first you are measuring the others against and add your equal sign, then add the possible options. The calculator will tell you if they are equivalent.

Your first option is (3 * x)^4.

(3x)4

=(3x)4

=3x*3x*3x*3x

=81x4

Is 3^4 * 3^x = to 81x^4? Yep.

And so is 3^(4+x)

So your answers are B and E, if you're looking at what I think you are looking at...

Be smart. Pass math. You got this.

What can you say about the graph of the function F(x) = (0.5)^x?

What can you say about the graph of the function F(x) = (0.5)^x?

A. Is it decreasing?

B. Is the x-intercept (0,1)?

C. Is the domain of F(x) x> 0?

D. Is the range of F(x) y > 0?

Answer: A. It is decreasing, and D. the range of F(x) y > 0.

Do you believe me?

Well let's graph it and see if these answers hold true.

Looks good to me...what do you think?

Simplify the Radical Equation sqrt x/25

A radical beard from publicdomainreview.org

Simplify the radical expression √x/25.

Okie dokie.

Answer: A. sqrt of x/5

I so like coffee...

A population of bacteria is changing exponentially - How can you describe the bacteria population?

Bacteria
Image from Wikimedia Commons, and is in Public Domain

A population of bacteria is changing exponentially according to the function below. How can you describe the bacteria population?

Select all possible correct answers.

B(t) = 400(1.4)^0.8t + 2

A. The population is decaying.

B. The population is approaching a constant value.

C. The population is always positive.

D. The population is growing.

Answers: C and D.

Hot damn! Now where's my coffee?

Evaluate 3^-3

Evaluate 3−3.  

Okay, can do. Check it out:

3^-3=

=

1

3*3*3

=

1

33

=

1

27

(Decimal: 0.037037) 

Easy peasy. Now, buy me a cup of coffee, if it helped;)

This Graph Could Be Which Exponential Function?

The graph below could be which exponential function?





A. F(x) = -4(1.1)5x


B. F(x) = 1.1(4)x


C. F(x) = 4(1.1)5x


D. F(x) = 4(1.1)-x

Figure it out by going to MathPapa.com and comparing graphs. Input your various options:

F(x) = 4(1.1)^(5x). Well what do you know?

The answer looks like C to me...what do you think?;)

Need a question figured out in a hurry? Buy me a cup of coffee, and send your question. I'll get back to you lightning fast, even in the middle of the night! Oh, a cup of coffee is about $3.00, so...

In general, the coordinates (0,a) will be a solution to the function F(x) = a⋅b^x.

In general, the coordinates (0,a) will be a solution to the function F(x) = a⋅b^x.

Is this true? Well here are your choices:

A. (b, 0)

B. (0, 0)

C. (0, a)

D. (a, b)

If x = 0, then b^x = b^0 = 1, so F(0) = a*1, so the coordinates (0,a) form a solution.

Answer: C. (0,a)

Need a question figured out in a hurry? Buy me a cup of coffee, and send your question. I'll get back to you lightning fast, even in the middle of the night! Oh, a cup of coffee is about $3.00, so...

How much would $140 invested at 6% interest compounded monthly be worth after 15 years?

How much would $140 invested at 6% interest compounded monthly be worth after 15 years? Round your answer to the nearest cent.

A(t) = P (1+r/n)^rt

A. $266.00

B. $335.52

C. $343.57

D. $150.88

The answer is C: $140 invested at 6% interest compounded monthly be worth $343.57 after 15 years.

Need a question figured out in a hurry? Buy me a cup of coffee, and send your question. I'll get back to you lightning fast, even in the middle of the night! Oh, a cup of coffee is about $3.00, so...

How much would $125 invested at 8% interest compounded continuously be worth after 16 years?

How much would $125 invested at 8% interest compounded continuously be worth after 16 years? Round your answer to the nearest cent.

A(t) = P * e^rt


A. $367.26

B. $428.24

C. $449.58

D. $285.00


How much would $125 invested at 8% interest compounded continuously be worth after 16 years?


Plug all values into the equation to find your answer:




A(t) = 125e^(.08 * 16) = $449.58


The answer is C: $449.58


Apex sucks. Math doesn't when you can apply it to daily life!

Need a question figured out in a hurry? Buy me a cup of coffee, and send your question. I'll get back to you lightning fast, even in the middle of the night! Oh, a cup of coffee is about $3.00, so...

What are the domain and range for the exponential function F(x) = 4^x + 3?

A. Domain: All real numbers

    Range: All real numbers greater than 3

B. Domain: All real numbers greater than 0

    Range: All real numbers greater than 0

C. Domain: All real numbers

    Range: All real numbers greater than 0

D. Domain: All real numbers greater than 0

    Range: All real numbers greater than 3

Answer: A. Domain: All real numbers

                  Range: All real numbers greater than 3

Have fun, math is easy when you know how to find the answers!

What can we say about the graph of the function F(x) = 4(7^x)?

A. The y-intercept is (0,7)

B. The range of F(x) is all real numbers.

C. The y-intercept is (0,4)

D. The y-intercept is (0,7)

Answer: What can we say about the graph of the function F(x) = 4(7x)?
We can say the y-intercept is (0,7).

Do the math. Then play a game. Just be sure to have fun doing both!

How to Express 0.000332 in Scientific Notation

Using the formula 3.32*10^-4:

3.32(10−4)

=3.32*10−4

=3.32*

1

10*10*10*10

=0.000332


Try the algebra calculator at the MathPapa site. It's awesome: 

http://www.mathpapa.com/algebra-calculator.html?q=3.32*10%5E-4

How much would $100 invested at 8% interest compounded annually be worth after 15 years?

Rounding our answer to the nearest cent and using the compound interest formula: A = P(1 + i)^n, and considering the following:

• P is the initial principle, 
• i is the annual rate of interest expressed as a decimal fraction, and 
• n is the number of years. 

Assuming annual compounding, the easiest way to approach this involves logs.

Plug in your numbers.


A = 100(1.08)^15


Log(A) = Log(100) + 15Log(1.08)

Log(A) = 2 + 15(0.0334237555) = 2.50135633

A = 10^2.50135633 = 317.21691


or about $317.22

Answer: How much would $100 invested at 8% interest compounded annually be worth after 15 years? $317.22

Eat snacks. Read a book. Kick Apex's ass.