natural logarithm - its logarithm to the base of the mathematical constant e

Formula: e^{Ln(x)}= x

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuousl

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = 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 20 years
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get:
V = [B]896.12[/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]

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

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded contin

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent.
[URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get:
A = [B]1,521.96[/B]