natural number - the positive integers (whole numbers)

Formula: 1, 2, 3, ...

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will t

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Set up the depreciation equation D(t) where t is the number of years in the life of the car:
D(t) = 24,000/(1.3)^t
The problem asks for D(t)<=7300
24,000/(1.3)^t = 7300
Cross multiply:
7300(1.3)^t = 24,000
Divide each side by 7300
1.3^t = 24000/7300
1.3^t = 3.2877
Take the natural log of both sides:
LN(1.3^t) = LN(3.2877)
Using the natural log identities, we have:
t * LN(1.3) = 1.1902
t * 0.2624 = 1.1902
Divide each side by 0.2624
t = 4.5356
[B]Rounding this up, we have t = 5[/B]

A natural number greater than 1 has only itself and 1 as factors is called

A natural number greater than 1 has only itself and 1 as factors is called a [B]prime number.[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuou

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get:
V = 96,300 * e^(0.028 * 7)
V = 96,300 * e^0.196
V = 96,300 * 1.21652690533
V = [B]$117,151.54[/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, t

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies?
We set up our exponential function where n is the number of days after today:
Z(n) = 25 * 2^n
We want to know n where Z(n) = 25,000.
25 * 2^n = 25,000
Divide each side of the equation by 25, to isolate 2^n:
25 * 2^n / 25 = 25,000 / 25
The 25's cancel on the left side, so we have:
2^n = 1,000
Take the natural log of each side to isolate n:
Ln(2^n) = Ln(1000)
There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have:
n * Ln(2) = Ln(1,000)
0.69315n = 6.9077
[URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]n = 9.9657 days ~ 10 days[/B]

Collatz Conjecture

Takes any natural number using the Collatz Conjecture and reduces it down to 1.

Lagrange Four Square Theorem (Bachet Conjecture)

Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.

Logarithms and Natural Logarithms and Eulers Constant (e)

This calculator does the following:

* Takes the Natural Log base e of a number x Ln(x) → log_{e}x

* Raises e to a power of y, e^{y}

* Performs the change of base rule on log_{b}(x)

* Solves equations in the form b^{cx} = d where b, c, and d are constants and x is any variable a-z

* Solves equations in the form ce^{dx}=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z

* Exponential form to logarithmic form for expressions such as 5^{3} = 125 to logarithmic form

* Logarithmic form to exponential form for expressions such as Log_{5}125 = 3

* Takes the Natural Log base e of a number x Ln(x) → log

* Raises e to a power of y, e

* Performs the change of base rule on log

* Solves equations in the form b

* Solves equations in the form ce

* Exponential form to logarithmic form for expressions such as 5

* Logarithmic form to exponential form for expressions such as Log

Natural Logarithm Table

Generates a natural logarithm table for the first (n) numbers rounded to (r) digits

Natural Numbers

Shows a set amount of natural numbers and cumulative sum

natural numbers that are factors of 16

natural numbers that are factors of 16
Natural numbers are positive integers starting at 1.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
Of these, [URL='https://www.mathcelebrity.com/factoriz.php?num=16&pl=Show+Factorization']the only factors of 16[/URL] are:
{[B]1, 2, 4, 8, 16}[/B]

Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?

Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?
The formula for the number of numbers including A to B is:
B - A + 1
With A = 1 and B = k, we have:
k - 1 + 1
[B]k[/B]

P is the natural numbers that are factors of 25

P is the natural numbers that are factors of 25
we type in [I][URL='https://www.mathcelebrity.com/factoriz.php?num=25&pl=Show+Factorization']factor 25[/URL][/I] into our math engine and we get:
{1, 5, 25}
Since [U]all[/U] of these are natural numbers, our answer is:
[B]{1, 5, 25}[/B]

Rational,Irrational,Natural,Integer Property

This calculator takes a number, decimal, or square root, and checks to see if it has any of the following properties:

* Integer Numbers

* Natural Numbers

* Rational Numbers

* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

* Integer Numbers

* Natural Numbers

* Rational Numbers

* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

Sum of the First (n) Numbers

Determines the sum of the first (n)

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x.
[U]Use the quotient remainder theorem[/U]
A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B
Plugging in our numbers for Equation 1 we have:
[LIST]
[*]A = x
[*]B = 7
[*]Q = q
[*]R = 6
[*]x = 7 * q + 6
[/LIST]
Plugging in our numbers for Equation 2 we have:
[LIST]
[*]A = x
[*]B = 11
[*]Q = q
[*]R = 2
[*]x = 11 * q + 2
[/LIST]
Set both x values equal to each other:
7q + 6 = 11q + 2
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=7q%2B6%3D11q%2B2&pl=Solve']equation calculator[/URL], we get:
q = 1
Plug q = 1 into the first quotient remainder theorem equation, and we get:
x = 7(1) + 6
x = 7 + 6
[B]x = 13[/B]
Plug q = 1 into the second quotient remainder theorem equation, and we get:
x = 11(1) + 2
x = 11 + 2
[B]x = 13[/B]

the set of natural numbers less than 7 that are divisible by 3

the set of natural numbers less than 7 that are divisible by 3
Natural Numbers less than 7
{1, 2, 3, 4, 5, 6}
Only 2 of them are divisible by 3. Divisible means the number is divided evenly, with no remainder:
[B]{3, 6}[/B]

the sum of 3 consecutive natural numbers, the first of which is n

the sum of 3 consecutive natural numbers, the first of which is n
Natural numbers are counting numbers, so we the following expression:
n + (n + 1) + (n + 2)
Combine n terms and constants:
(n + n + n) + (1 + 2)
[B]3n + 3
Also expressed as 3(n + 1)[/B]

the sum of 3 consecutive natural numbers, the first of which is n

the sum of 3 consecutive natural numbers, the first of which is n
We have:
n + (n + 1) + (n + 2)
Grouping like terms, we have:
[B]3n + 3[/B]

The sum of 3 consecutive natural numbers, the first of which is n

The sum of 3 consecutive natural numbers, the first of which is n.
We have 3 numbers:
n, n + 1, and n + 2
Add them up:
n + (n + 1) + (n + 2)
Group like terms:
[B]3n + 3[/B]

X is a natural number greater than 6

I saw this ticket come through today.
The answer is x > 6.
Natural numbers are positive numbers not 0. So 1, 2, 3, ...
Let me build this shortcut into the calculator.
Also, here is the[URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E6&pl=Show+Interval+Notation'] interval notation[/URL] for that expression.