Vocabulary
Natural base e- An irrational number defined as follows: As n approaches +∞, (1+(1/n)^n approaches e≈2.718281828.
Essential Information
Throughout history special numbers have been discovered such as ∏ or i. e is another special number and is called the natural base e, or the Euler number.
Natural base expressions can be simplified as regular exponents.
e²⋅e⁵=e²⁺⁷=e⁷ (12e⁴)/(3e³)=4e⁴⁻³=4e (5e⁻³ⁿ)²=5²(e⁻³ⁿ)²=25e⁻⁶ⁿ=25/(e⁶ⁿ)
Or you can use a calculator:
Natural base expressions can be simplified as regular exponents.
e²⋅e⁵=e²⁺⁷=e⁷ (12e⁴)/(3e³)=4e⁴⁻³=4e (5e⁻³ⁿ)²=5²(e⁻³ⁿ)²=25e⁻⁶ⁿ=25/(e⁶ⁿ)
Or you can use a calculator:
Natural Base Functions
A function of the form y=ae^(rx) is called a natural base exponential function
A function of the form y=ae^(rx) is called a natural base exponential function
- If a>0 and r>0, the function is an exponential growth function.
- If a>0 and r<0, the function is an exponential decay function.
Continuously Compounded Interest
The formula A=P(1+(r/n)^nt is used model an account earning compound interest. As the frequency n of compounding approaches +∞, the compound interest formula approximates the following formula.
A = Pe^(rt)
where P is the principal and r is the annual interest rate expressed as a decimal.
The formula A=P(1+(r/n)^nt is used model an account earning compound interest. As the frequency n of compounding approaches +∞, the compound interest formula approximates the following formula.
A = Pe^(rt)
where P is the principal and r is the annual interest rate expressed as a decimal.